Question

What root of x does the expression (x^3/8)^2/3 yield?

square root
cube root
fourth root
eighth root

Answer 1

The rule for exponents of exponents is:

a^b^c=a^(b*c), in this case:

x^(3/8)^(2/3)

x^((3/8)*(2/3))

x^(6/24)

x^(1/4)

So x^(1/4) is equal to the fourth root.

Answer 2

Fourth root.

Explanation:

The given expression is :
`(x^{(3)/(8) })^{(2)/(3) }`

The power rule for exponents states that powers are multiplied

`(a^(m))^(n) =a^(mn)`

Applying the rule we have:

`(a^{(3)/(8) }) ^{(2)/(3) } =a^{(3)/(8) .(2)/(3) } =a^{(1)/(4) }`

So the x root of the expression will represent the fourth root.