Which expression is equivalent to - -a2b1-2 -1 -

The correct option is D 1ab^1/4 The value of [ √(a^2b^1/2) #10;]^ 1=((a^2b^1/2)^1/2)^ 1 =(a^2× 1/2 b^1/2× #10;1/2)^ 1 =(ab^1/4)^ 1=a^ 1 ...

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Standard IX

Mathematics

Surds

Which express...

Question

Which expression is equivalent to ${[\sqrt{a^{2} b^{\frac{1}{2}}}]}^{- 1}$ ?

a^{- 2} b^{\frac{- 1}{2}}

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- a b^{\frac{1}{4}}

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- a b^{2}

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\frac{1}{a b^{\frac{1}{4}}}

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Solution

The correct option is D $\frac{1}{a b^{\frac{1}{4}}}$
The value of ${[\sqrt{a^{2} b^{\frac{1}{2}}}]}^{- 1} = ((a^{2} b^{\frac{1}{2}})^{1 / 2})^{- 1}$
$= (a^{2 \times 1 / 2} b^{1 / 2 \times 1 / 2})^{- 1}$
$= (a b^{1 / 4})^{- 1} = a^{- 1} b^{- \frac{1}{4}}$
$= \frac{1}{a b^{\frac{1}{4}}}$

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Which expression is equivalent to [√a2b12]−1 ?

The correct option is D 1ab14The value of [√a2b12]−1=((a2b12)1/2)−1=(a2×1/2b1/2×1/2)−1=(ab1/4)−1=a−1b−14=1ab14

Which expression is equivalent to ${[\sqrt{a^{2} b^{\frac{1}{2}}}]}^{- 1}$ ?

The correct option is D $\frac{1}{a b^{\frac{1}{4}}}$
The value of ${[\sqrt{a^{2} b^{\frac{1}{2}}}]}^{- 1} = ((a^{2} b^{\frac{1}{2}})^{1 / 2})^{- 1}$
$= (a^{2 \times 1 / 2} b^{1 / 2 \times 1 / 2})^{- 1}$
$= (a b^{1 / 4})^{- 1} = a^{- 1} b^{- \frac{1}{4}}$
$= \frac{1}{a b^{\frac{1}{4}}}$