Question

Sort the following numbers in increasing order of their power of '4' from top to bottom.

• A. $(4^{-3}{)}^2$
• B. $4^3\times 4^2$
• C. $2^2\times 8^2$
• D. $(4^2{)}^{-2}$

Answer 1

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.
$\therefore$ $(4^{-3}{)}^2=4^{-6}$
Here power of '4' is : $-6$

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.
$\therefore$ $4^3\times 4^2=4^5$
Here power of '4' is : $5$

By using law of exponents:
$a^m\times b^m=(ab{)}^m$
$\text{here a and b are base, and m is the exponent}$.
$\therefore 2^2\times 8^2=(2\times 8{)}^2$
$={16}^2$
$=(4\times 4{)}^2$
$=(4^2{)}^2$
$=4^4$
Here power of '4' is : $4$

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.
$\therefore$ $(4^2{)}^{-2}=4^{-4}$
Here power of '4' is : $-4$