Question

Simplify: ${(2^5÷2^8)}^5$ × $2^{-5}$

• A. 1/2¹⁰
• B. 1/2²⁰
• C. 1/2^(-15)
• D. 1/2^(-5)

Answer 1

The correct option is B

1/2²⁰

${(2^5÷2^8)}^5$ × $2^{-5}$
= ${\left(\frac{2^5}{2^8}\right)}^5$ ×$2^{-5}$
= ${\left(2^{5-8}\right)}^5$× $2^{-5}$
= ${\left(2^{-3}\right)}^5$ × $2^{-5}$
= $2^{-15-5}$
= $2^{-20}$
= $\frac{1}{2^{20}}$