Question

Match these parts of laws of exponents with their equivalent counterparts.

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

Answer 1

We can multiply or divide two powers with different base and same exponents by multiplying or dividing the bases respectively.

So, $a^m\times b^m=(ab{)}^m$

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

We can multiply or divide two powers with same base and different exponents by adding or subtracting the exponents respectively.

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

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