Solution of both enrichment questions Q 1 If 9x×32×3-x2-2=127, find x Q 2 By what number should - Maths - Exponents and Powers

Question

Solution of both enrichment questions
Q 1 If 9 x × 3 2 × 3 - x 2 - 2 = 1 27 , find x
Q 2 By what number should - 3 2 - 3 be divided so that the quotient
may be - 8 27 - 2

Shruti Tyagi · Accepted Answer

Dear student,

Question 1)9x×32×3-x2-2=127⇒32x×32×3-x2×-2=133         --[using amn=am×n]⇒32x×32×3x=3-3             --[using a-m=1am]⇒33x+2=3-3          --[using am×an=am+n]Comparing powers as the base is same⇒3x+2=-3⇒3x=-3-2⇒3x=-5⇒x=-53
Question 2)Let -32-3 be divided by A to get -827-2⇒ -32-3÷A= -827-2⇒-233×1A= -2782                  --[using a-m=1am]⇒1A= -2782 ×-323⇒1A= -33232 ×-323⇒1A= -3232 ×-323               --[using ambm=abm]⇒1A= -326 ×-323                   --[using amn=am×n]⇒1A= -326+3                              --[using am×an=am+n]⇒1A= -329⇒A= -239                                   --[by reciprocal]Thus the value of A is -239

Regards

Solution of both enrichment questions Q.1. If 9 x × 3 2 × 3 - x 2 - 2 = 1 27 , find x. Q.2. By what number should - 3 2 - 3 be divided so that the quotient may be - 8 27 - 2 .

Solution of both enrichment questions
Q.1. If $9^{x} \times 3^{2} \times {(3^{\frac{- x}{2}})}^{- 2} = \frac{1}{27}$ , find x.
Q.2. By what number should ${(\frac{- 3}{2})}^{- 3}$ be divided so that the quotient may be ${(\frac{- 8}{27})}^{- 2}$ .