Question

If a = b²÷³ and b= c-²


,then what is the value of a in terms of c ?​

Answer 1

Given that,

$a = {b}^{\frac{2}{3}}$ ...(A)

$b = c^{-2}$

Now, continuing from A,

$a = {b}^{\frac{2}{3}}$

Putting the value of b in terms of c,

⇒ $a = {({c}^{-2})}^{\frac{2}{3}}$

We know, ${({a}^m)}^{n} = {a}^{mn}$

∴ $a = {c}^{-2 \times \frac{2}{3}}$

⇒ $a = {c}^{\frac{-4}{3}}$

Now we also know, ${a}^{-n} = \dfrac{1}{{a}^{n}}$ & ${a}^{\frac{m}{n}} = \sqrt[n]{a^m}$.

∴ $a = c^{\frac{-4}{3}}$

⇒ $a = \frac{1}{c^{\frac{4}{3}}}$

⇒ $\boxed{a = \frac{1}{\sqrt[3]{{c}^{4}}} }$.

So, (C) is the correct option.