Question

Which one among the following is correct?

• A. ${\left(\frac{a}{b}\right)}^m$ = $\frac{\left(b^m\right)}{\left(a^m\right)}$
• B. ${\left(\frac{a}{b}\right)}^m$ = a
• C. ${\left(\frac{a}{b}\right)}^m$ = $\frac{\left(a^m\right)}{\left(b^m\right)}$
• D. ${\left(\frac{a}{b}\right)}^{-m}$ = $b^m$$a^m$

Answer 1

The correct option is C

${\left(\frac{a}{b}\right)}^m$ = $\frac{\left(a^m\right)}{\left(b^m\right)}$

${\left(\frac{a}{b}\right)}^m$ = $\frac{a}{b}$ × $\frac{a}{b}$ × .........(m times )

=$\frac{a\times a\times a..........\left(mtimes\right)}{b\times b\times b..........\left(mtimes\right)}$

= $\frac{a^m}{b^m}$