Question

If $x$ be any integer different from zero and $m,n$ be any integers, then ${\left(x^m\right)}^n$ is equal to

• A. $x^{m-n}$
• B. $x^{m+n}$
• C. $x^{mn}$
• D. $x^{\frac{m}{n}}$

Answer 1

The correct option is C $x^{mn}$

Using laws of exponents,

${\left(a^m\right)}^n={\left(a\right)}^{m\times n}$ [when $a\ne 0$]

Similarly, $\therefore \left({\left(x^m\right)}^n\right)={\left(x\right)}^{mn}$

Hence, the correct option is (B).