What is the expression in simplest radical form? (5x^(4) y^(3))^{(2)/(9) }

Question

What is the expression in simplest radical form?

`(5x^(4) y^(3))^{(2)/(9) }`

Answer 1

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

1. Fractional exponents to radicals:
   `x^(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)^(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}`

Answer 2

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