Without calculating exact values

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Without calculating exact values, decide which of the two expressions is greater:

6^{\frac{3}{4}}\times36^{\frac{1}{4}}

216^{\frac{1}{2}}

. (a)

6^{\frac{3}{4}}\times36^{\frac{1}{4}}

is greater (b)

216^{\frac{1}{2}}

is greater (c) Both expressions are equal (d)

6^{\frac{3}{4}}\times36^{\frac{1}{4}}

is exactly half of

216^{\frac{1}{2}}