Question

Evaluate [(64) ^1/2]^1/3​

Answer 1

Step-by-step explanation:

$({64}^{ \frac{1}{2} } ) ^{ \frac{1}{3} } \\ 8 ^{ \frac{1}{3} } \\ 2$

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

concept:

Here , Exponent and Power concept is used.

64 can also be written as 4³ or as $2 \times 2 \times 2 \times 2 \times 2 \times 2$ or 2⁶

Tips for solving such Question:-

=>For solving such Question full of powers and brackets we need to first identify the Middle value have exponential term or not.

=>After we clear that middle value have exponential term just convert into power notation.

=>After we convert into power notation or into exponential form we will evaluate it easily.

By using exponential and power we will evaluate this question :

$\huge\implies\:{ {( {(64}^{ \frac{1}{2} } )}^{ \frac{1}{3} } )}$

$\huge\implies\:{ { {( {2}^{6}) }^{ \frac{1}{2} } )}^{ \frac{1}{3} } }$

$\huge\implies\:{ {( {2}^{ \frac{6}{2} } )}^{ \frac{1}{3} } = { ({2}^{3} )}^{ \frac{1}{3} }}$

$\huge\implies\:$$\huge{ {( {2}^{3} )}^{ \frac{1}{3} } = {(2)}^{ \frac{3}{3} } = 2}$

$\huge\therefore$$\huge\bold{2 \:is \:our\: answer}$