Simplify-a 23 -3- 23 -1b - -12 -3 -2

(a) The given product can be written as nbsp; ( 23 )^ 3× ( 23 )^ 1= ( 23 )^ 3+( 1)= ( 23 )^ 4= ( 32 )^4=8116 (b) The exponent nbsp; [ ( 12 )^ 3 ]^ 2 ca ...

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Byju's Answer

Standard VIII

Mathematics

Division of Exponents Having the Same Base

Simplify:a 23...

Question

Simplify:
(a) ${(\frac{2}{3})}^{- 3} \times {(\frac{2}{3})}^{- 1}$
(b) ${[{(\frac{- 1}{2})}^{- 3}]}^{- 2}$

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Solution

(a) The given product can be written as -
${(\frac{2}{3})}^{- 3} \times {(\frac{2}{3})}^{- 1} = {(\frac{2}{3})}^{- 3 + (- 1)} = {(\frac{2}{3})}^{- 4} = {(\frac{3}{2})}^{4} = \frac{81}{16}$

(b) The exponent ${[{(\frac{- 1}{2})}^{- 3}]}^{- 2}$ can be written as ${(\frac{- 1}{2})}^{[(- 3) \times (- 2)]} = {(\frac{- 1}{2})}^{6} = \frac{1}{64}$

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2 \frac{1}{4} \div \frac{2}{7} o f 1 \frac{1}{3} \times \frac{2}{3}

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${[\frac{- 1 + \sqrt{(- 3)}}{2}]}^{3 n}$ + ${[\frac{- 1 - \sqrt{(- 3)}}{2}]}^{3 n}$

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Q. The value of

\sqrt{3 - 2 \sqrt{2}}

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Simplify: (a) (23)−3×(23)−1 (b) [(−12)−3]−2

(a) The given product can be written as - (23)−3×(23)−1=(23)−3+(−1)=(23)−4=(32)4=8116 (b) The exponent [(−12)−3]−2 can be written as (−12)[(−3)×(−2)]=(−12)6=164

Simplify:
(a) ${(\frac{2}{3})}^{- 3} \times {(\frac{2}{3})}^{- 1}$
(b) ${[{(\frac{- 1}{2})}^{- 3}]}^{- 2}$