Simplify : [(3√(6√(5^9)))]^4 [(6√(3√(5^9)))]^4

Question

Simplify :

\(\bigg[\sqrt[3]{\sqrt[6]{5^9}}\bigg]^4\bigg[\sqrt[6]{\sqrt[3]{5^9}}\bigg]^4\)

(a) 5² 

(b) 5⁴ 

(c) 5⁸ 

(d) 5¹²

Answer 1

(b) 5⁴ 

\(\bigg[\sqrt[3]{\sqrt[6]{5^9}}\bigg]^4\bigg[\sqrt[6]{\sqrt[3]{5^9}}\bigg]^4\)

= \(5^{9\times\frac16\times\frac13\times4}\times5^{9\times\frac13\times\frac16\times4}\)

= 5² x 5² = 5⁴ .