Mathematics

Problem

Prove the following identity for any positive real number

a

\sqrt[3]{a}\,\sqrt[6]{a} = a^{\frac{1}{2}}.

Then use the identity to evaluate the product when

a = 64

. a. (i) Express both radicals on the left-hand side in exponential form. b. (ii) Using the laws of exponents, simplify the product to obtain the right-hand side of the identity. c. (iii) Substitute

a = 64

and compute the numerical value of each side to verify the identity.

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