If a = b^(2/3) and b = c^(–2) , what is the value of a in terms of c ?

Question

If a = \(b^{\frac23}\) and b = c^–2, what is the value of a in terms of c ?

(a) \(\frac{4}{c^3}\)

(b) \(\sqrt[3]{c^4}\)

(c) \(\frac{1}{\sqrt[3]{c^4}}\)

(d) \(\sqrt[4]{c^3}\)

Answer 1

(c) \(\frac{1}{\sqrt[3]{c^4}}\)

a = \(b^{\frac{2}{3}}\) and b = c^-2

∴ a = (c^-2)^{\({\frac{2}{3}}\)} = c^\(-\frac43\) = \(\frac{1}{c^{\frac43}}\) = \(\frac{1}{\sqrt[3]{c^4}}\)