Question

$a^m\times a^n$ is equal to

• A. ${\left(a^2\right)}^{mn}$
• B. $a^{m-n}$
• C. $a^{m+n}$
• D. $a^{mn}$

Answer 1

The correct option is C

$a^{m+n}$

Since the base $a$ is same and power $m$ and $n$ are different.

When we multiply two numbers with same base but different powers, then according to law of exponents the base remains same and power adds.

Therefore,

$a^m\times a^n={\left(a\right)}^{m+n}$

So, ${\mathit{a}}^{\mathbf{m}}\mathbf{\times }{\mathit{a}}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{m}\mathbf{+}\mathbf{n}}$.

Hence, the correct option is (c).