Question

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

Answer 1

Answer:

Fourth root.

Step-by-step explanation:

The given expression is :$(x^{\frac{3}{8} })^{\frac{2}{3} }$

The power rule for exponents states that powers are multiplied

$(a^{m})^{n} =a^{mn}$

Applying the rule we have:

$(a^{\frac{3}{8} }) ^{\frac{2}{3} } =a^{\frac{3}{8} .\frac{2}{3} } =a^{\frac{1}{4} }$

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

Answer 2

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.