Question

Rationalize the denominator and simplify
8x/ ^5sqrt(27x^17y^13)
Is the answer 8^5sqrt(9x^3y^2)/3x^4y^3)

Answer 1

Is this your question?
\[\frac{8x}{\sqrt[5]{27x^17y^13}}\]

Answer 2

Yes

Answer 3

Let's simplify it
\[\frac{8x}{\sqrt[5]{27x^{17}y^{13}}}\]
Let's write x and y 's powers as multiples of 5
\[\frac{8x}{\sqrt[5]{27x^{15}x^2y^{10}y^3}}\]
We get now
\[\frac{8x}{x^3y^2\sqrt[5]{27x^2y^3}}\]
Now if we want to remove root from the denominator then we need to multiply
\((\sqrt[5]{27x^2y^3})^4\) to both numerator and denominator
We get
\[\frac{8x \times (\sqrt[5]{27x^2y^3})^4}{x^3y^2(27x^2y^3)}\]
We get
\[\frac{8x \times (\sqrt[5]{27x^2y^3})^4}{27x^5y^5}\]
Now we get
\[\frac{8 \times (\sqrt[5]{27x^2y^3})^4}{27x^4y^5}\]