Question

What is the radical form of the expression (2x^4y^5)^3/8

Answer 1

We are given expression: $(2x^4y^5)^{3/8}$

Let us distribute 3/8 over exponents in parenthesis, we get

$(2^{3/8}x^{4\times 3/8}y^{5\times 3/8}) = (2^{3/8}x^{12/8}y^{15/8})$

$= (2^{3/8}x^{1\frac{4}{8}} y^{1\frac{7}{8}} )$

We can get x and y out of the radical because, we get whlole number 1 for x and y exponents for the mixed fractions.

So, we could write it as.

$(2^{3/8}x^{1\frac{4}{8}} y^{1\frac{7}{8}} ) = xy(2^{\frac{3}{8} }x^{\frac{4}{8}} y^{\frac{7}{8}} )$

Now, we could write inside expression of parenthesis in radical form.

$xy\sqrt[8]{2x^{3}x^4y^7}$