The correct options are B nbsp;(64) ^ 2 C (4) ^ 6 D (2) ^ 12Using nbsp;(a/b)^m =(a^m)/(b^m), we get, (1/64) ^2 = 1^2/64 ^2 = 1/64^2 Using nbsp;a^ m=1/ ...

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Byju's Answer

Standard VII

Mathematics

a^m / b^m = (a/b)^m

1/642=

Question

$(\frac{1}{64})^{2}$ =

(4)^{- 3}

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(64)^{- 2}

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(4)^{- 6}

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(2)^{- 12}

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Solution

The correct options are
B $(64)^{- 2}$
C $(4)^{- 6}$
D $(2)^{- 12}$
Using ${(\frac{a}{b})}^{m} = \frac{(a^{m})}{(b^{m})}$ , we get,

$(\frac{1}{64})^{2} = \frac{1^{2}}{64^{2}} = \frac{1}{64^{2}}$

Using $a^{- m} = \frac{1}{a^{m}}$ , we can write
$\frac{1}{64^{2}}$ = $(64)^{- 2}$

But $(64)^{- 2}$
$= (4^{3})^{- 2}$
$= (4)^{3 \times - 2}$ $[∵ (a^{m})^{n} = a^{m n}]$
$= (4)^{- 6}$

Similarly, we can write
$(4)^{- 6} = (2^{2})^{- 6} = (2)^{2 \times - 6} = (2)^{- 12}$

$∴ (\frac{1}{64})^{2} = (64)^{- 2} = (4)^{- 6} = (2)^{- 12}$

Suggest Corrections

(164)2 =

$(\frac{1}{64})^{2}$ =