Question

If $x$ be any non-zero integer and $m,n$ be negative integers, then $x^m\times x^n$ is equal to:

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

Answer 1

The correct option is B

$x^{m+n}$

Explanation for correct option:

Find the value of the given exponent

Using the law of exponents,

$a^m\times a^n=a^{m+n}$

where $a$ is a non-zero integer and $m,n$ be any integer.

It means that we need to add the exponents when same bases are multiplied.

Thus, $x^m\times x^n=x^{m+n}$

For example, $3^5\times 3^7=3^{5+7}=3^{12}$

Hence, option (B), $x^{m+n}$ is the correct answer.