The correct option is C 1/16 We know that (a^m)^n=a^mn . (256)^ 1/2= nbsp;(2^8)^ 1/2 (Since 256 = 2 × nbsp; 2 × nbsp; 2 × nbsp; 2 × nbsp; 2 × nbsp ...

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Standard VIII

Mathematics

Power of a Power

Simplify 256-...

Question

Simplify ${(256)}^{\frac{- 1}{2}}$ .

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$\frac{1}{16}$

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$\frac{1}{4}$

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Solution

The correct option is C
$\frac{1}{16}$

We know that ${(a^{m})}^{n} = a^{m n}$ .
${(256)}^{\frac{- 1}{2}} = {(2^{8})}^{\frac{- 1}{2}} (Since 256 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^{8})$
$= 2^{(8 \times (\frac{- 1}{2}))}$
$= 2^{- 4}$
$= \frac{1}{16}$

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Similar questions

Simplify $\frac{4}{{(216)}^{- 2 / 3}} + \frac{1}{{(256)}^{- 3 / 4}} + \frac{2}{{(243)}^{- 1 / 5}}$

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{log}_{\sqrt{2}} 256

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{(256)}^{- (4 - \frac{3}{2})}

Q. Simplify:

\frac{3}{216^{- 2 / 3}} + \frac{2}{256^{- 3 / 4}} + \frac{2}{243^{- 1 / 5}}

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\frac{4}{2187^{\frac{- 3}{7}}} - \frac{5}{256^{\frac{- 3}{4}}} + \frac{4}{{{[1331]}^{2}}^{\frac{- 1}{3}}}

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Simplify (256)−12.

The correct option is C 116 We know that (am)n=amn . (256)−12=(28)−12 (Since 256=2×2×2×2×2×2×2×2=28 ) =2(8×(−12)) =2−4 =116

Simplify ${(256)}^{\frac{- 1}{2}}$ .

The correct option is C
$\frac{1}{16}$

We know that ${(a^{m})}^{n} = a^{m n}$ .
${(256)}^{\frac{- 1}{2}} = {(2^{8})}^{\frac{- 1}{2}} (Since 256 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^{8})$
$= 2^{(8 \times (\frac{- 1}{2}))}$
$= 2^{- 4}$
$= \frac{1}{16}$