(64)^ 23=(4^3)^ 23=4^ 2 (14)^ 3=(4^ 1)^ 3=4^3 (64)^ 23×(14)^ 3=4^ 2× 4^3=4^3 2=4^1 =4 . ...

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Byju's Answer

Standard VIII

Mathematics

Multiplication of Any Polynomial

64-2/3× 1/4 -...

Question

$(64)^{\frac{- 2}{3}} \times {(\frac{1}{4})}^{- 3}$

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Solution

$(64)^{- \frac{2}{3}} = (4^{3})^{- \frac{2}{3}} = 4^{- 2}$
${(\frac{1}{4})}^{- 3} = (4^{- 1})^{- 3} = 4^{3}$
$(64)^{- \frac{2}{3}} \times {(\frac{1}{4})}^{- 3} = 4^{- 2} \times 4^{3} = 4^{3 - 2} = 4^{1}$
$= 4$ .

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Evaluate: ${(\begin{matrix} \frac{64}{125} \end{matrix})}^{\frac{- 2}{3}} \div \frac{1}{(\frac{256}{625})^{\frac{1}{4}}} + (\begin{matrix} \frac{(\sqrt{25})}{\sqrt[3]{64}} \end{matrix})$

In ch .1

A question

to simplify

64^1/3(64^1/3 - 64^2/3)

in this the solution is given as

= (4^3)^ -1/3[ ( 4^3)^1/3 - (4^3)^2/3 ]

how -1/3 came ?

{(64)}^{\frac{- 2}{3}} \times {(\frac{1}{4})}^{- 3}

equals

Q. Simplify:

(64)^{- \frac{2}{3}} \times {(\frac{1}{4})}^{- 3}

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(64)−23×(14)−3

(64)−23=(43)−23=4−2(14)−3=(4−1)−3=43(64)−23×(14)−3=4−2×43=43−2=41=4.

$(64)^{\frac{- 2}{3}} \times {(\frac{1}{4})}^{- 3}$

$(64)^{- \frac{2}{3}} = (4^{3})^{- \frac{2}{3}} = 4^{- 2}$
${(\frac{1}{4})}^{- 3} = (4^{- 1})^{- 3} = 4^{3}$
$(64)^{- \frac{2}{3}} \times {(\frac{1}{4})}^{- 3} = 4^{- 2} \times 4^{3} = 4^{3 - 2} = 4^{1}$
$= 4$ .