Question

Evaluate the numerical expression the quantity 2 to the power of five sixths end quantity over the quantity 2 to the power of one sixth end quantity.

cube root of 4
cube root of 2
square root of 8
square root of 6

Answer 1

The calculated value of the numerical expression
`2^\frac56 / 2^\frac16` is a. cube root of 4

How to evaluate the numerical expression

From the question, we have the following parameters that can be used in our computation:

the quantity 2 to the power of five sixths end quantity over the quantity 2 to the power of one sixth end quantity.

This means that

`2^\frac56 / 2^\frac16`

Applying the law of indices, we have

`2^\frac56 / 2^\frac16 = 2^(\frac56 - \frac16)`

So, we have

`2^\frac56 / 2^\frac16 = 2^(\frac46)`

Simplify

`2^\frac56 / 2^\frac16 = 2^(\frac23)`

This can be further expressed as

`2^\frac56 / 2^\frac16 = 4^(\frac13)`

`2^\frac56 / 2^\frac16 = \sqrt[3]{4}`

Hence, the numerical expression is cube root of 4