NCERT Solutions for Class 7 Maths Chapter 11 - Exponents & Powers

Share with your friends Share Share Share twitter

Answer:

[(–3)²]³
= (–3)^2×3  
= (–3)⁶  

Hence, the correct answer is option B.                

Answer:

For a non-zero rational number x, x⁸ ÷ x² is equal to
x⁸ ÷ x²
= x^8-2 
= x⁶
Hence, the correct answer is option B.

Answer:

x is a non-zero rational number. Product of the square of x (x²)with the cube of x(x³) is equal to the 
(x²) × (x³) = (x⁶)  

So, the product of the square of x with the cube of x is equal to the sixth power of x.
Hence, the correct answer is option D.
 

Answer:

For any two non-zero rational numbers x and y, x⁵ ÷ y⁵ is equal to
 x⁵ ÷ y⁵ =  ${\left(\frac{x}{y}\right)}^5$ = ${\left(x÷y\right)}^5$

Hence, the correct answer is option C.
 

Answer:

a^m ×aⁿ is equal to a^m+n
Hence, the correct answer is option C.
 

Answer:

(1⁰ + 2⁰ + 3⁰) is equal to 1 + 1 + 1 = 3

Hence, the correct answer is option C.

Answer:

$\frac{{10}^{22} + {10}^{20}}{{10}^{20}}$
$$\begin{gathered} =\frac{{10}^{20}\left({10}^{22-20} + 1\right)}{{10}^{20}} \\ ={10}^{22-20}+1 \\ ={10}^2 +\hspace{0.17em}1 \\ =100 + 1 \\ =101 \end{gathered}$$

Hence, the correct answer is option C.

Answer:

The standard form of the number 12345 is 1.2345 × 10⁴
Hence, the correct answer is option D.
 

Answer:

If 2¹⁹⁹⁸ – 2¹⁹⁹⁷ – 2¹⁹⁹⁶ + 2¹⁹⁹⁵ = K.2¹⁹⁹⁵, then the value of K is
^{$$\begin{gathered} 2^{1998} – 2^{1997} – 2^{1996} + 2^{1995} = K.2^{1995} \\ \Rightarrow 2^{1995}\left( 2^3-2^2-2+1\right)=K.2^{1995} \\ \Rightarrow \left(2^3-2^2-2+1\right)=K \\ \Rightarrow \left(8-4-2+1\right)=K \\ \Rightarrow K=3 \end{gathered}$$}
Hence, the correct answer is option C.

 

Answer:

2⁰ + 3⁰ + 4⁰ = 1 + 1 + 1 = 3
2⁰ × 3⁰ × 4⁰= 1 × 1 × 1 = 1
(3⁰ – 2⁰) × 4⁰= (1 - 1) × 1 = 0
(3⁰ – 2⁰) × (3⁰ + 2⁰) = (1 - 1) × (1 + 1) = 0

Hence, the correct answer is option B.


 

Answer:

In standard form, the number 72105.4 is written as 7.21054 × 10ⁿ where n is equal to
72105.4 = 7.21054 × 10⁴
n = 4
Hence, the correct answer is option C.
 

Answer:

Square of  $\left(\frac{-2}{3}\right)$ = ${\left(\frac{-2}{3}\right)}^2=\frac{-2}{3}\times \frac{-2}{3}=\frac{-2\times -2}{3\times 3}=\frac{4}{9}$
Hence, the correct answer is option D.

Answer:

Cube of $\left(\frac{-1}{4}\right)$=${\left(\frac{-1}{4}\right)}^3=\frac{-1}{4}\times \frac{-1}{4}\times \frac{-1}{4}=\frac{-1\times -1\times -1}{4\times 4\times 4}=\frac{-1}{64}$
Hence, the correct answer is option C.

Answer:

${\left(\frac{-5}{4}\right)}^4=\frac{{\left(-5\right)}^4}{{\left(4\right)}^4}=\frac{\left(-5\right)\times \left(-5\right)\times \left(-5\right)}{4\times 4\times 4}=\frac{-5}{4}\times \frac{-5}{4}\times \frac{-5}{4}\times \frac{-5}{4}$

Hence, the correct answer is option C

Answer:

$\frac{2^4}{{\left(7^0+3^0\right)}^3}=\frac{2^4}{{\left(1+!\right)}^3}=\frac{2^4}{{\left(2\right)}^3}=2^{4-3}=2$

Hence, the correct answer is option D.

Answer:

${\left(\frac{2}{3}\right)}^3\times {\left(\frac{5}{7}\right)}^3$= ${\left(\frac{2}{3}\times \frac{5}{7}\right)}^3$
Hence, the correct answer is option C.

Answer:

 829030000 =  8.29030000 × 10⁸

In standard form, the number 829030000 is written as K × 10⁸ where K is equal to 8.2903.
Hence, the correct answer is option D.

Answer:

$\frac{1}{1000}$=0.001 has the largest value.

Hence, the correct answer is option B.

Answer:

72 crore = 72,00,00,000 = 7.2 × 10⁸
Hence, the correct answer is option C.

 

Answer:

For non-zero numbers a and b, ${\left(\frac{a}{b}\right)}^m$ ÷ ${\left(\frac{a}{b}\right)}^n$ = ${\left(\frac{a}{b}\right)}^{m-n}$ where m > n.
Hence, the correct answer is option C.

Answer:

3³ = 27 ≠ 9

Hence, the correct answer is option C.

Answer:

 8 is equal to 2³
8² = (2³)²  = 2⁶

So, 2 is the power of 8 which is equal to 2⁶
Hence, the correct answer is option B.
 

Answer:

(–2)³¹ × (–2)¹³ = (–2)³¹⁺¹³ = (–2)<sup>44    

So,  44 will make the statement true.</sup>

Answer:

(–3)⁸ ÷ (–3)⁵ = (–3)^8-5 = (–3)³ 

Answer:

${\left(\frac{11}{15}\right)}^4\times {\left(\frac{11}{15} \right)}^5={\left(\frac{11}{5}\right)}^9$

Answer:

${\left(\frac{-1}{4}\right)}^3\times \left(\frac{-1}{4}\right) \times {\left(\frac{-1}{4}\right)}^7 ={\left(\frac{-1}{4}\right)}^{11}$

Answer:

${\left[{\left(\frac{7}{11}\right)}^3\right]}^4={\left(\frac{7}{11}\right)}^{12} =\left(\frac{7}{11}\right) \times {\left(\frac{7}{11}\right)}^{11}$

Answer:

${\left(\frac{6}{13}\right)}^{10}÷ {\left[{\left(\frac{6}{13}\right)}^5\right]}^2={\left(\frac{6}{13}\right)}^{10}÷ {\left(\frac{6}{13}\right)}^{10}=1 = \frac{6}{13}÷\frac{6}{13}$

Answer:

${\left[{\left(\frac{-1}{4}\right)}^{16}\right]}^2={\left(\frac{-1}{4}\right)}^{16\times 2}={\left(\frac{-1}{4}\right)}^{32}=\left(\frac{-1}{4}\right)\times {\left(\frac{-1}{4}\right)}^{31}$

Answer:

${\left(\frac{13}{14}\right)}^5÷ {\left(\frac{13}{14} \right)}^2={\left(\frac{13}{14}\right)}^3$

Answer:

$a^6 \times a^5 \times a^0 = a^{11} \times 1=a^{11}=a\times a^{10}$

Answer:

1 lakh = 1,00,000 = 10 × 10⁴

Answer:

1 million = 10,00,00,000 = 10 × 10⁷

Answer:

$729=3^6$

Answer:

$432 = 2^4 \times 3^2$

Answer:

$53700000 =5.37 \times {10}^7$

Answer:

$88880000000=8.888\times {10}^{10}$

Answer:

$27500000 = 2.75 \times {10}^7$

Answer:

$340900000 = 3.409 \times {10}^8$

Answer:

(a) 3² = 9
So, 3² < 15

(b) 2³  = 8, 3² = 9
So, 2³ < 3²

(c) 7⁴  = 2401 , 5⁴ = 625
7⁴ > 5⁴

(d) 10⁵= 100000  
10,000 < 10⁵

(e) 6³ = 216, 4⁴ = 216  
6³ = 4⁴

Answer:

One million = 1000000 = 10⁶

Answer:

One hour = 60 minutes = 3600 seconds = 60² seconds

Answer:

1⁰ × 0¹ = 1 × 0 = 0

So, the given statement is true. 

Answer:

(–3)⁴ = 81

So, the given statement is false.
 

Answer:

​3⁴ = 3 × 3 × 3 × 3 = 81
4³ = 4 × 4 × 4 = 64

3⁴ > 4³
Hence, the given statement is true.
 

Answer:

LHS = ${\frac{\left(-3\right)}{5}}^{100}$
RHS = ${\left(\frac{-3}{5}\right)}^{100}$

Clearly, LHS is not equal to RHS.
Hence, the given statement is false.

Answer:

(10 + 10)¹⁰ = (20)¹⁰   ≠ 10¹⁰ + 10¹⁰

Hence, the given statement is False.

Answer:

x⁰ × x⁰ = 1 × 1 = 1 ÷ 1 = 1
which is true for all non-zero values of x.

Hence, the given statement is true.

Answer:

ans

Answer:

4² = 16 and 2⁴ = 16

So, 4² is equal to 2⁴.
Hence, the given statement is true.

Answer:

x^m + x^m = 2x^m , where x is a non-zero rational number and m is a positive integer.

Hence, the given statement is false.

Answer:

x^m × y^m = (x × y)^m, where x and y are non-zero rational numbers and m is a positive integer

Hence, the given statement is false.

Answer:

$x^m ÷ y^m=\frac{x^m}{y^m}={\left(\frac{x}{y}\right)}^m= {(x ÷ y)}^m$, where x and y are non-zero rational numbers and m is a positive integer.
Hence, the given statement is true.

Answer:

x^m × xⁿ means x is multiplied m + n times, which is equal to x^m + n where x is a non-zero rational number and m, n are positive integers.

Hence, the given statement is true.

Answer:

4⁹ is = $4^9={\left(4^2\right)}^4\times 4={16}^4\times 4 >\hspace{0.17em}{16}^3$

Hence, the given statement is true.

Answer:

${\left(\frac{2}{3}\right)}^3÷{\left(\frac{5}{2}\right)}^3=\frac{\left(\frac{2}{3}\right)\times \left(\frac{2}{3}\right)\times \left(\frac{2}{3}\right)}{\left(\frac{5}{2}\right)\times \left(\frac{5}{2}\right)\times \left(\frac{5}{2}\right)}=\frac{2\times 2\times 2\times 2\times 2\times 2}{3\times 3\times 3\times 5\times 5\times 5}\ne 1$

Hence, the given statement is false.

Answer:

${\left(\frac{4}{3}\right)}^5\times {\left(\frac{5}{7}\right)}^5={\left(\frac{4\times 5}{3\times 7}\right)}^5\ne {\left(\frac{4}{3}+\frac{5}{7}\right)}^5$

Hence, the given statement is false.

Answer:

${\left(\frac{5}{8}\right)}^9÷{\left(\frac{5}{8}\right)}^4={\left(\frac{5}{8}\right)}^{9-4}={\left(\frac{5}{8}\right)}^5$

Hence, the given statement is false.

Answer:

${\left(\frac{7}{3}\right)}^2\times {\left(\frac{7}{3}\right)}^5={\left(\frac{7}{3}\right)}^{2+5}={\left(\frac{7}{3}\right)}^7\ne {\left(\frac{7}{3}\right)}^{10}$

Hence, the given statement is false.

Answer:

5⁰ × 25⁰ × 125⁰ = 1× 1× 1 = 1
And, (5⁰)⁶ = 1⁶ = 1

Hence, the given statement is true.

Answer:

876543 = 800000 + 70000 + 6000 + 500 + 40 + 3
            = 8 × 10⁵ + 7 × 10⁴ + 6 × 10³ + 5 × 10² + 4 × 10¹ + 3 × 10⁰

Hence, the given statement is True.

Answer:

600060 = 600000 + 60 = 6 × 10⁵ + 6 × 10 ≠ 6 × 10⁵ + 6 × 10²

Hence, the given statement is False.

Answer:

4 × 10⁵ + 3 × 10⁴ + 2 × 10³ + 1 × 10⁰ = 400000 + 30000 + 2000 + 1 = 432001 ≠ 432010.

Hence, the given statement is false.

Answer:

8 × 10⁶ + 2 × 10⁴ + 5 × 10² + 9 × 10⁰ = 8000000 + 20000 + 500 + 9 = 8020509.

Hence, the given statement is true.

Answer:

LHS = 4⁰ + 5⁰ + 6⁰ = 1 + 1 + 1 = 3
RHS = (4 + 5 + 6)⁰ = 1
Clearly, LHS is not equal to RHS.

Hence, the given statement is false.

Answer:

2⁵= 2 × 2 × 2 × 2× 2 = 32
3³ = 3 × 3 × 3 = 27
2³× 2 = 2 × 2 × 2 × 2 = 16
(3³)² =  3³× 3³ = 27 × 27 = 729
3⁵ = 3³ × 3² = 243
4⁰ = 1
2³×3¹ = 24

4⁰,  2³×3¹ , 2³× 2,  3³ , 2⁵, 3⁵,  (3³)²  is in ascending order

 

Answer:

2²⁺³ = 2⁵ = 32,
(2²)³ = 2⁶ = 64
2 × 2² = 2³ = 8
$\frac{3^5}{3^2}$= 3³ = 27 
3² × 3⁰ = 9 
2³ × 5² = 200

2³ × 5² ,  (2²)³ , 2²⁺³ , $\frac{3^5}{3^2}$, 3² × 3⁰ , 2 × 2²  is in descending order.

 

Answer:

(– 4)⁵  ÷ (– 4)³  =  (– 4)²   
So, (– 4)⁵  should be divided by (– 4)²  so that the quotient may be equal to (– 4)³ .

Answer:

${\left(\frac{2}{9}\right)}^3\times {\left(\frac{2}{9}\right)}^6$ $={\left(\frac{2}{9}\right)}^{2m-1}$
⇒${\left(\frac{2}{9}\right)}^{3+6}$ $={\left(\frac{2}{9}\right)}^{2m-1}$
⇒ ${\left(\frac{2}{9}\right)}^9$ $={\left(\frac{2}{9}\right)}^{2m-1}$
⇒ 2m - 1 = 9
⇒ 2m = 10
⇒ m = 5

 

Answer:

$\frac{p}{q}={\left(\frac{3}{2}\right)}^2÷{\left(\frac{9}{4}\right)}^0$
$$\begin{gathered} \Rightarrow \frac{p}{q}={\left(\frac{3}{2}\right)}^2÷1 = {\left(\frac{3}{2}\right)}^2 \\ \Rightarrow {\left(\frac{p}{q}\right)}^3={\left[{\left(\frac{3}{2}\right)}^2\right]}^3={\left(\frac{3}{2}\right)}^6 \end{gathered}$$

Answer:

$$\begin{gathered} {\left(\frac{1}{2}\right)}^2÷{\left(\frac{2}{3}\right)}^3 \\ ={\left(\frac{1}{2}\right)}^2\times {\left(\frac{3}{2}\right)}^3 \\ ={\left(\frac{1}{2}\right)}^2\times {\left(\frac{3}{2}\right)}^3 \end{gathered}$$
The reciprocal of the rational number $1÷\left[{\left(\frac{1}{2}\right)}^2\times {\left(\frac{3}{2}\right)}^3\right]$.
$$\begin{gathered} =1\times \frac{1}{\left[{\left(\frac{1}{2}\right)}^2\times {\left(\frac{3}{2}\right)}^3\right]} \\ =\frac{1}{\left[{\left(\frac{1}{2}\right)}^2\times {\left(\frac{3}{2}\right)}^3\right]} \\ =\frac{32}{27} \end{gathered}$$

Answer:

(a) 7⁰  = 1
(b) 7⁷ ÷ 7⁷  = 1
(c) (–7)^{2 × 7 – 6 – 8} = (–7)⁰ = 1 
(d) (2⁰ + 3⁰ + 4⁰) (4⁰ – 3⁰ – 2⁰)= (1 + 1 + 1)(1 – 1 – 1) = 3 × –1 = –3
(e) 2 × 3 × 4 ÷ 2⁰ × 3⁰ × 4⁰  = 24 ÷ 1 = 24
(f) (8⁰ – 2⁰) × (8⁰ + 2⁰) = (1 – 1) × (1 + 1) = 0

Answer:

2^n–5 × 6^2n–4 = $\frac{1}{{12}^4\times 2}$
⇒2^n–5 × 6^2n–4 = $\frac{1}{{12}^4\times 2}$
⇒2^n–5 × (2 × 3)^2n–4 = $\frac{1}{{12}^4\times 2}$
⇒ 2^n–5+2n-4 × (3)^2n–4 = $\frac{1}{{\left(3\times 4\right)}^4\times 2}$

⇒ 2^3n-9× (3)^2n–4 = ${\left(3\right)}^{-4}\times {\left(2\right)}^{-9}$

⇒ 3n - 9 = 9
⇒ n = 0

 

Answer:

(a) 8.01 × 10⁷ = 80100000
(b) 1.75 × 10^–3= 0.0017
 

Answer:

(a) 2⁵ = 31
(b) (-3⁵) =  -243
(c) -(-4)⁴ =  -256

Answer:

(a) 3 × 3 × 3 × a × a × a × a
= 3³ × a⁴

(b) a × a × b × b × b × c × c × c × c
= a² × b³ × c⁴

(c) s × s × t × t × s × s × t
=  s⁴ × t ³

Answer:

Let x be the number of times 30 be added together to get a sum equal to 30⁷
So, 30 × x = 30⁷ 
⇒ $x=\frac{ {30}^7}{30}={30}^6$

Answer:

(a) 1024
= 2¹⁰

(b) 1029
= 3 × 7³

(c) $\frac{144}{875}$ 
= $\frac{{12}^2}{5^3\times 7}$

Answer:

(a) 2⁶ or 6²
2⁶ = 64 or 6²  = 36
2⁶ > 6²  

(b) 2⁹ or 9²
2⁹ = 512 or 9²  = 81
2⁶ >  9² 

(c) 7.9 × 10⁴ or 5.28 × 10⁵
7.9 × 10⁴ = 79000 or 5.28 × 10⁵ = 528000
7.9 × 10⁴  < 5.28 × 10⁵





 

Answer:

(a) 9000 = 3² × 10³
(b) 2025 = 5² × 3⁴
(c) 800 = 2³ × 10²

Answer:

(a) 2³ × 3³ = 6³
(b) 2⁴ × 4² = 2⁴ × (2)⁴ = (2)⁸
(c) 5² × 7² = 35² 
(d) (– 5)⁵ × (–5) = (– 5)⁶
(e) (– 3)³ × (– 10)³= (30)³
(f) (– 11)² × (– 2)² = (22)²

Answer:

(a) 76,47,000 = 7.647 × 10⁶
(b) 8,19,00,000 = 8.19 × 10⁷
(c) 5, 83,00,00,00,000 = 5.83 × 10¹¹
(d) 24 billion = 2.4× 10¹⁰

Answer:

The speed of light in vaccum is 3 × 10⁸ m/s.
Sunlight takes about 8 minutes = 8 × 60 = 480 seconds to reach the earth.
The distance of Sun from Earth in standard form = Speed × Time = 3 × 10⁸ m/s × 480 s = 1.44  × 10¹¹ m

Answer:

$$\begin{gathered} \left(\mathrm{a}\right) \left[{\left(\frac{3}{7}\right)}^4\times {\left(\frac{3}{7}\right)}^5\right]÷{\left(\frac{3}{7}\right)}^7= {\left(\frac{3}{7}\right)}^9÷{\left(\frac{3}{7}\right)}^7={\left(\frac{3}{7}\right)}^{9-7}={\left(\frac{3}{7}\right)}^2 \\ \left(\mathrm{b}\right) \left[{\left(\frac{7}{11}\right)}^5÷{\left(\frac{7}{11}\right)}^2\right]\times {\left(\frac{7}{11}\right)}^2={\left(\frac{7}{11}\right)}^3\times {\left(\frac{7}{11}\right)}^2={\left(\frac{7}{11}\right)}^5 \\ \left(\mathrm{c}\right) {\left(3^7÷3^5\right)}^4={\left(3^2\right)}^4=3^8 \\ \left(\mathrm{d}\right) \left(\frac{a^6}{a^4}\right)\times a^5\times a^0=\left(a^2\right)\times a^5\times 1=a^7 \\ \left(\mathrm{e}\right) \left[{\left(\frac{3}{5}\right)}^3\times {\left(\frac{3}{5}\right)}^8\right]÷\left[{\left(\frac{3}{5}\right)}^2\times {\left(\frac{3}{5}\right)}^4\right]= {\left(\frac{3}{5}\right)}^{11}÷{\left(\frac{3}{5}\right)}^6={\left(\frac{3}{5}\right)}^5 \\ \left(\mathrm{f}\right) \left(5^{15}÷5^{10}\right)\times 5^5=\left(5^{15-10}\right)\times 5^5=5^5\times 5^5=5^{10} \end{gathered}$$

Answer:

$$\begin{gathered} \left(\mathrm{a}\right) \frac{7^8\times a^{10}{b}^7{c}^{12}}{7^6\times a^8{b}^4{c}^{12}}=\left(7^{8-6}\right)\times \left(a^{10-8}\right)\left(b^{7-4}\right)\left(c^{12-12} \right)= \left(7^2\right)\times \left(a^2\right)\left(b^3\right)\left(c^0 \right) \\ \left(\mathrm{b}\right) \frac{5^4\times 7^4\times 2^7}{8\times 49\times 5^3}=\left(5^{4-3}\right)\times \left(7^{4-2}\right)\left(2^{7-3}\right)= \left(5^1\right)\times \left(7^2\right)\times \left(2^4\right) \\ \left(\mathrm{c}\right) \frac{125\times 5^2\times a^7}{{10}^3\times a^4}=\frac{5^3\times 5^2\times a^7}{5^3\times 2^3\times a^4}=\left(5^{5-3}\right)\times \left(a^{7-4}\right)\times \left(2^{-3}\right)=\left(5^2\right)\times \left(a^3\right)\times \left(2^{-3}\right) \\ \left(\mathrm{d}\right) \frac{3^4\times {12}^3\times 36}{2^5\times 6^3}=\frac{3^4\times 3^3\times 2^6\times 6^2}{2^5\times 6^3}= 3^7\times 2^{6-5}\times 6^{2-3}= 3^7\times 2^1\times 6^{-1} \\ \left(\mathrm{e}\right) {\left(\frac{6\times 10}{2^2\times 5^3}\right)}^2\times \frac{25}{27} = {\left(\frac{2\times 3\times 2\times 5}{2^2\times 5^3}\right)}^2\times \frac{5\times 5}{3^3} = {\left(3\times 5^{1-3}\right)}^2\times \frac{5^2}{3^3}={\left(\frac{3}{5^2}\right)}^2\times \frac{5^2}{3^3}=\frac{1}{5^2\times 3} \\ \left(\mathrm{f}\right) \frac{{15}^4\times {18}^3}{3^3\times 5^2\times {12}^2}=\frac{3^4\times 5^4\times 6^3\times 3^3}{3^3\times 5^2\times 6^2\times 2^2}=3^{7-3}\times 5^{4-2}\times 6^{3-2}=3^4\times 5^2\times 6^1 \\ \left(\mathrm{g}\right) \frac{6^4\times 9^2\times {25}^3}{3^2\times 4^2\times {15}^6}=\frac{3^4\times 2^4\times 3^2\times 3^2\times 5^6}{3^2\times 3^6\times 2^4\times 5^6}=3^{8-8}\times 2^{4-4}\times 5^{6-6} = 1 \end{gathered}$$

Answer:

Answer:

Answer:

Answer:

In our own planet Earth, 361,419,000 square kilometre of area is covered with water and  square kilometre of area is covered by land.
The approximate ratio of area covered with water to area covered by land by converting these numbers into scientific notation
$$\begin{gathered} =\frac{361,419,000}{148,647,000} \\ =\frac{361,419 \times {10}^3}{148,647\times {10}^3} \\ =\frac{120,473}{49,549} \end{gathered}$$
 

Answer:

2ⁿ⁺² – 2ⁿ⁺¹ + 2ⁿ = c × 2ⁿ
⇒2ⁿ(2² – 2 + 1) = c × 2ⁿ
⇒2ⁿ(2² – 2 + 1) = c × 2ⁿ
⇒2ⁿ(3) = c × 2ⁿ
⇒c = 3  
 

Answer:

(a) 1 light year = 9,460,000,000,000 km = 9.46 × 10¹³ km
(b) The average distance between Earth and Sun is 1.496 × 10⁸ km.
Clearly, 9.46 × 10¹³ km > 1.496 × 10⁸ km,
The distance between Earth and the Sun less than one light year


 

Answer:

The number of diagonals of an n-sided figure is $\frac{1}{2}$(n² –3n).
The formula to find the number of diagonals for a 6-sided figure (hexagon)
=  $\frac{1}{2}$[6² – (3×6)]
= $\frac{1}{2}$[36 – (18)]
= 9

Answer:

Bacteria can divide in every 20 minutes. So 1 bacterium can multiply to 2 in 20 minutes. 4 in 40 minutes, and so on. How many bacteria will there be in 6 hours

Number of times it doubles itself = $\frac{360}{20}=18$

Number of bacteria will there be in 6 hours = 2 × 2 × 2 × 2× 2.........× 2 = 2¹⁸
 

Answer:

2² × 3² × 5 × 17
= 4 × 9 × 5 × 17
= 180 × 17
= 3060 kg 
 

Answer:

A typical red blood cell has a diameter of approximately 7 × 10^–6 metres.
A typical platelet has a diameter of approximately 2.33 × 10^–6 metre. 

As 7 × 10^–6 metres > 2.33 × 10^–6 metre

Red blood cell has a greater diameter than the diameter of the platelet.
 

Answer:

(a) Googol can be written as a power as: 
$1\times {10}^{100}$

(b) Googol times a googol written as a power as:
$1\times {10}^{100 }\times 1\times {10}^{100}=1\times \left({10}^{100+100}\right)=1\times {10}^{200}$

Answer:

As $\frac{3^5}{9^5}$ is the same as $\frac{3^5}{9^5}={\left(\frac{1}{3}\right)}^5\ne \frac{1}{3}$ . 
So, student made the mistake in writing the power of the resultant.