Question

Evaluate: ${\left(\frac{1}{2}\right)}^{-3}{\left(\frac{1}{4}\right)}^{-2}{\left(\frac{1}{16}\right)}^{-1}$

• A. ${\left(\frac{1}{2}\right)}^{-48}$
• B. ${\left(\frac{1}{2}\right)}^{-11}$
• C. ${\left(\frac{1}{2}\right)}^{-6}$
• D. ${\left(\frac{1}{8}\right)}^{-11}$
• E. ${\left(\frac{1}{8}\right)}^{-6}$

Answer 1

The correct option is B ${\left(\frac{1}{2}\right)}^{-11}$

$={\left(\frac{1}{2}\right)}^{-3}\times {\left(\frac{1}{4}\right)}^{-2}\times {\left(\frac{1}{16}\right)}^{-1}$

$={\left(\frac{1}{2}\right)}^{-3}\times {\left(\frac{1}{4}\right)}^{-2}\times {\left(\frac{1}{16}\right)}^{-1}$

$=\left(\frac{1}{2^{-3}}\right)\times \left(\frac{1}{2^{-4}}\right)\times \left(\frac{1}{2^{-4}}\right)$

$=\left(\frac{1}{2^{-3-4-4}}\right)$

$=\left(\frac{1}{2^{-11}}\right)$

$={\left(\frac{1}{2}\right)}^{-11}$