Cube root of√(cube root of√a^3) is equal to (a) a (b) 1 (c) a^1/3 (d) a^3

Question

\(\sqrt[3]{\sqrt[3]{a^3}}\) is equal to

(a) a

(b) 1

(c) \(a^\frac{1}{3}\)

(d) a³

Answer 1

(c) \(a^{\frac{1}{3}}\)

\(\sqrt[3]{\sqrt[3]{a^3}}\) = \(\big((a^3)^{\frac{1}{3}\big)^{\frac{1}{3}}}\) = \(a^{3\times\frac{1}{9}}\) = \(a^{\frac{1}{3}}\)