Simplify 81-16-3-4-25-9-3-2-5-2-3-

Simplify the given expression:[ (81/16)^ 3/4×[(25/9)^ 3/2÷(5/2)^ 3]; =(3^4/2^4)^ 3/4×[(5^2/3^2)^ 3/2÷( ...

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Byju's Answer

Standard VII

Mathematics

Exponents with Unlike Bases and Same Exponent

Simplify 81/1...

Question

Simplify ${(\frac{81}{16})}^{- \frac{3}{4}} \times [{(\frac{25}{9})}^{- \frac{3}{2}} \div {(\frac{5}{2})}^{- 3}]$

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Solution

Simplify the given expression:
$\begin{array}{l} {(\frac{81}{16})}^{- \frac{3}{4}} \times [{(\frac{25}{9})}^{- \frac{3}{2}} \div {(\frac{5}{2})}^{- 3}] \\ = {(\frac{3^{4}}{2^{4}})}^{- \frac{3}{4}} \times [{(\frac{5^{2}}{3^{2}})}^{- \frac{3}{2}} \div {(\frac{5}{2})}^{- 3}] \\ = {(\frac{3}{2})}^{- 3} \times [{(\frac{5}{3})}^{- 3} \div {(\frac{5}{2})}^{- 3}] [∵ {(a^{m})}^{n} = a^{m \times n}] \\ = {(\frac{2}{3})}^{3} \times [{(\frac{3}{5})}^{3} \div {(\frac{2}{5})}^{3}] [∵ (a^{- m}) = \frac{1}{a^{m}}] \\ = {(\frac{2}{3})}^{3} \times [{(\frac{3}{5})}^{3} \times {(\frac{5}{2})}^{3}] \\ = 1 \end{array}$
Hence,the value of the given expression is ${(\frac{81}{16})}^{- \frac{3}{4}} \times [{(\frac{25}{9})}^{- \frac{3}{2}} \div {(\frac{5}{2})}^{- 3}] = 1$

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Simplify 8116−34×259−32÷52−3

Simplify the given expression:8116−34×259−32÷52−3=3424−34×5232−32÷52−3=32−3×53−3÷52−3∵amn=am×n=233×353÷253∵a-m=1am=233×353×523=1Hence,the value of the given expression is 8116−34×259−32÷52−3=1

Simplify ${(\frac{81}{16})}^{- \frac{3}{4}} \times [{(\frac{25}{9})}^{- \frac{3}{2}} \div {(\frac{5}{2})}^{- 3}]$