Question

Simplify the following :
${\left(\frac{-1}{2}\right)}^5\times 2^6\times {\left(\frac{3}{4}\right)}^3$

• A. $\frac{27}{11}$
• B. $\frac{27}{32}$
• C. $\frac{7}{32}$
• D. $-\frac{27}{32}$

Answer 1

Answer: (D)

$-\frac{27}{32}$

Given, ${\left(\frac{-1}{2}\right)}^5\times 2^6\times {\left(\frac{3}{4}\right)}^3$

=$\left(\frac{-1}{2^5}\right)\times 2^6\times \left(\frac{3^3}{4^3}\right)$

=$\left(-1\right)\times 2^{6-5}\times \left(\frac{3^3}{4^3}\right)$

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

=$\left(-1\right)\times 2\times \left(\frac{3^3}{2^6}\right)$

=$\left(-1\right)\times 2^{1-6}\times 3^3$

=$\left(-1\right)\times 2^{-5}\times 3^3$

=$\left(-1\right)\times 2^{-5}\times 27$

=$\left(-1\right)\times \frac{1}{2^5}\times 27$

=$\frac{-27}{32}$