Question

Match the following power with their corresponding power.

• A. $729$
• B. $3125$
• C. $100$
• D. $\frac{1}{4}$

Answer 1

By using law of exponent:
$a^m\times a^n=a^{m+n}$, here $a$ is called base and $m,n$ are called powers. If base is same then powers are added together.
$\therefore$ $2^{-5}\times 2^3=2^{-2}$
$=(\frac{1}{2}{)}^2$
$=\frac{1}{2}\times \frac{1}{2}$
$=\frac{1}{4}$

By using law of exponents:
$a^m\times b^m=(ab{)}^m$
$\text{here a and b are base, and m is the exponent}$.
$\therefore 2^2\times 5^2=(2\times 5{)}^2$
$={10}^2$
$=100$

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.
$\therefore$ $(3^2{)}^3=3^6$
$=3\times 3\times 3\times 3\times 3\times 3$
$=(3\times \times 3\times 3)\times (3\times \times 3\times 3)$
$27\times 27$
$=729$

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.
$\therefore \frac{{15}^5}{3^5}=(\frac{15}{3}{)}^5$
$=5^5$
$=5\times 5\times 5\times 5\times 5$
$=(5\times 5\times 5)\times (5\times 5)$
$=125\times 25$
$=3125$