Question

If $\frac{a}{b}={\left(\frac{1}{2}\right)}^{-3}\times {\left(\frac{5}{6}\right)}^0,$ find the the value of ${\left(\frac{a}{b}\right)}^{-2}$

• A. $\frac{1}{74}$
• B. $\frac{1}{44}$
• C. $\frac{1}{4}$
• D. $\frac{1}{64}$

Answer 1

The correct option is D $\frac{1}{64}$

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

$\frac{a}{b}=(2{)}^3\times 1$

$\frac{a}{b}=8$

${\left(\frac{a}{b}\right)}^{-2}=(8{)}^{-2}=\frac{1}{8^2}$

${\left(\frac{a}{b}\right)}^{-2}=\frac{1}{64}$