Question

Simplify: ${\left(\frac{81}{16}\right)}^{\frac{-3}{4}}\times {\left(\frac{25}{9}\right)}^{\frac{-3}{2}}$

• A. $0.25$
• B. $0.064$
• C. $0.02$
• D. $1$

Answer 1

The correct option is B $0.064$

${\left(\frac{81}{16}\right)}^{\frac{-3}{4}}\times {\left(\frac{25}{9}\right)}^{\frac{-3}{2}}={\left[{\left(\frac{3}{2}\right)}^4\right]}^{\left(\frac{-3}{4}\right)}\times {\left[{\left(\frac{5}{3}\right)}^2\right]}^{\left(\frac{-3}{2}\right)}={\left(\frac{3}{2}\right)}^{4\times \frac{-3}{4}}\times {\left(\frac{5}{3}\right)}^{2\times \frac{-3}{2}}[\because (x^a{)}^b=x^{ab}]={\left(\frac{3}{2}\right)}^{-3}\times {\left(\frac{5}{3}\right)}^{-3}=(\frac{2^3}{3^3})\times (\frac{3^3}{5^3}\left)\right[\because {\left(\frac{x}{y}\right)}^a=\frac{x^a}{y^a}]=2^3\times \frac{1}{5^3}={\left(\frac{2}{5}\right)}^3=(\frac{8}{125})=0.064$