Question

What is the expression in simplest radical form?rac%7B2%7D%7B9%7D%20%7D" id="TexFormula1" title="(5x^{4} y^{3})^{\frac{2}{9} }" alt="(5x^{4} y^{3})^{\frac{2}{9} }" align="absmiddle" class="latex-formula">

Answer 1

Use the formula a^(x/n) = (n)√a^x   (note it is a small n)

(5x^4y^3)^(2/9) = Small 9

Convert.

$\sqrt{9{{(25x^{8})y^9 }}}$ is your answer

hope this helps

Answer 2

So here are a few things about exponents you should know:

1. Fractional exponents to radicals: $x^\frac{m}{n}=\sqrt[n]{x^m}$
2. Powering a power: $(x^m)^n=x^{m*n}$

So firstly, convert the fractional exponent to a radical:

$(5x^4y^3)^\frac{2}{9}=\sqrt[9]{(5x^4y^3)^2}$

Next, solve the outer power:

$\sqrt[9]{(5x^4y^3)^2} =\sqrt[9]{5^2x^{4*2}y^{3*2}} =\sqrt[9]{25x^8y^6}$

Your final answer is $\sqrt[9]{25x^8y^6}$