Question

Simplify ${(2^5÷2^8)}^5\times 2^{-5}$

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

Answer 1

The correct option is B

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

${(2^5÷2^8)}^5\times 2^{-5}$

$={\left(\frac{2^5}{2^8}\right)}^5\times 2^{-5}$

$={\left(2^{5-8}\right)}^5\times 2^{-5}[\because \frac{a^m}{a^n}=a^{m-n}]$

$={\left(2^{-3}\right)}^5\times 2^{-5}$

$=2^{-15}\times 2^{-5}[\because (a^m{)}^n=a^{mn}]$

$=2^{-15+(-5)}[\because a^m\times a^n=a^{m+n}]$

$=2^{-20}$

$=\frac{1}{2^{20}}[\because a^{-m}=\frac{1}{a^m}]$