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

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

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»

(c) \(\frac{1}{\sqrt[3]{c^4}}\)

a = \(b^{\frac{2}{3}}\) and b = c^-2

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