Simplify -1-216-2-3-1-27-4-3

Given (1/216)^ 2/3÷(1/27)^ 4/3[ (1/216)^ 2/3÷(1/27)^ 4/3=(1/6^3)^ 2/3÷(1/3^3)^ 4/3; =(6^ 3)^ 2/3÷(3^ 3)^ 4/3[∵(a^m)^n=a^mn]; ...

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Byju's Answer

Standard VII

Mathematics

Taking Power of a Power

Simplify :1/2...

Question

Simplify : ${(\frac{1}{216})}^{- \frac{2}{3}} \div {(\frac{1}{27})}^{- \frac{4}{3}}$

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Solution

Given ${(\frac{1}{216})}^{- \frac{2}{3}} \div {(\frac{1}{27})}^{- \frac{4}{3}}$
$\begin{matrix} {(\frac{1}{216})}^{- \frac{2}{3}} \div {(\frac{1}{27})}^{- \frac{4}{3}} = {(\frac{1}{6^{3}})}^{- \frac{2}{3}} \div {(\frac{1}{3^{3}})}^{- \frac{4}{3}} \\ = {(6^{- 3})}^{- \frac{2}{3}} \div {(3^{- 3})}^{- \frac{4}{3}} [∵ {(a^{m})}^{n} = a^{m n}] \\ = 6^{2} \div 3^{4} \\ = \frac{6 \times 6}{3 \times 3 \times 3 \times 3} \\ = \frac{4}{9} \end{matrix}$
Hence the simplified form of ${(\frac{1}{216})}^{- \frac{2}{3}} \div {(\frac{1}{27})}^{- \frac{4}{3}}$ is $\frac{4}{9}$ .

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