Question

If $a$ and $b$ are non-zero integers, $m$ and $n$ are any integers, then which of the following are true?

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

Answer 1

Answer: (B), (C), (D)

The correct options are
B $a^m\times a^n=a^{(m+n)}$
C $a^m\times b^m={\left(ab\right)}^m$
D $\frac{a^m}{b^m}={\left(\frac{a}{b}\right)}^m$

If $a$ and $b$ are non-zero integers, $m$ and $n$ are any integers, then

$\frac{a^m}{a^n}=a^{m-n},$

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

$a^m\times b^m={\left(ab\right)}^m$ and

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