Question

$2^{-3}\times 2^{-5}$ is equal to_______.

• A. $2^{-8}$
• B. $2^{-2}$
• C. $2^2$
• D. $\frac{1}{2^8}$

Answer 1

Answer: (A), (D)

The correct options are
A $2^{-8}$
D $\frac{1}{2^8}$

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.
$\therefore$ $2^{-3}\times 2^{-5}=2^{-8}$
Also same number can be expressed in different form that is,
$2^{-3}\times 2^{-5}=(\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2})\times (\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2})$
$=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}$
$=\frac{1}{2^8}\left(\text{by using above law}\right)$