Simplify -256-1-2-16-1-4-4-1-16-

The correct option is D 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 IX

Mathematics

Laws of Exponents

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

Suggest Corrections

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