Evaluate: $ 27^{-\frac{2}{3}} \times 9^{-\frac{1}{2}} \p 81^{-\frac{5}{4}} $"

Given: $27^{-\frac{2}{3}} \times 9^{-\frac{1}{2}} \div 81^{-\frac{5}{4}}$

To do: To evaluate $27^{-\frac{2}{3}} \times 9^{-\frac{1}{2}} \div 81^{-\frac{5}{4}}$

Solution:

As given expression: $27^{-\frac{2}{3}} \times 9^{-\frac{1}{2}} \div 81^{-\frac{5}{4}}$

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

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

$=3^{-2}\times3^{-1}\div3^{-5}$

$=3^{-2+( -1)-( -5)}$                       [$\because a^m\times a^n\times a^z=a^{m+n-z}$]

$=3^{-3+5}$

$=3^{2}$

$=9$

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Updated on: 10-Oct-2022

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