Question

Match the powers of '3' with their corresponding reduced powers.

• A. $3^6$
• B. $3^{-6}$
• C. $3^9$

Answer 1

By using law of exponent:
$\frac{a^m}{b^m}=(\frac{a}{b}{)}^m$ Here $a$ and $b$ is called the base and $m$ is called the exponent.
$\therefore (\frac{15}{5}{)}^6=3^6$

By using law of exponent:
$(a^m{)}^n=a^{mn}$ Here $a$ is called the base and $m,n$ are called the exponent. For Power of power exponents are multiplied if the base is same.
$\therefore$ $(3^{-3}{)}^2=3^{-6}$

By using law of exponents:
$a^m\times b^m=(ab{)}^m$
$\text{here a and b are base, and m is the exponent}$.
$\therefore 3^3\times 9^3={27}^3$
$=(3\times 3\times 3{)}^3$
$=(3^3{)}^3$
$=3^9$