MCQ
If $\text{a}=\frac{1}{\sqrt[3]{\text{b}}}$ ,then $b$ is:
  • A
    $\text{a}^3$
  • B
    $\sqrt{a}$
  • $\frac{1}{\text{a}^3}$
  • D
    $\sqrt[3]{a}$

Answer

Correct option: C.
$\frac{1}{\text{a}^3}$

Given $\text{a}=\frac{1}{\sqrt[3]{\text{b}}}$
$\Rightarrow \text{a}\frac{1}{(\text{b})^\frac{1}{3}}$
Cubing both the sides we get,
$\text{a}^3=\Bigg(\frac{1}{\text{b}^{\frac{1}{3}}}\Bigg)^3=\frac {1}{\text{b}}$
$\Rightarrow\text{b}=\frac{1}{\text{a}^3}$

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