Solve this:
Q.71. Find (- 1)$\times$(- 1)$\times$...... 2 m times, m is a natural number?
(A) - 1
(B) 1
(C) 2
(D) - 2

Dear Student,

The solution is as under:

$$\begin{gathered} \left(-1\right)\times \left(-1\right)\times \left(-1\right)\times ......2m times \\ or, ={\left(-1\right)}^{2m} \left\{in exponents, when base is same, power is added, a^m\times a^n=a^{m+n}\right\} \\ Now, as m is a natural number, and natural numbers are integers which starts from 1 and goes upto infinity, \\ hence 2m will be an even integer \\ or, ={\left(-1\right)}^{2m}=1 \left\{as {\left(-1\right)}^{even int}=1\right\} \end{gathered}$$

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