Question

Simplify ${(2^5÷2^8)}^5$ × $2^{-5}.$

• A. $\frac{1}{2^{20}}$
• B. $\frac{1}{2^{10}}$
• C. $\frac{1}{2^{(-15)}}$
• D. $\frac{1}{2^{(-5)}}$

Answer 1

The correct option is A

$\frac{1}{2^{20}}$

${(2^5÷2^8)}^5\times 2^{-5}={\left(\frac{2^5}{2^8}\right)}^5\times 2^{-5}$
$={\left(2^{5-8}\right)}^5\times 2^{-5}(\because \frac{a^m}{a^n}=a^{m-n})$
$={\left(2^{-3}\right)}^5\times 2^{-5}$
$=2^{-15}\times 2^{-5}(\because (a^m{)}^n=a^{mn})$
$=2^{-15-5}(\because a^m\times a^n=a^{m+n})$
$=2^{-20}$
$=\frac{1}{2^{20}}(\because a^{-m}=\frac{1}{a^m})$