Question

What is the simplified form of the fifth root of x to the fourth power times the fifth root of x to the fourth power

Answer 1

Answer:

$x^{\frac{8}{5}}$.

Step-by-step explanation:

We are asked to find the simplified form of expression: The fifth root of x to the fourth power times the fifth root of x to the fourth power.

First of all we will write an expression from our given information as:

$\sqrt[5]{x^4}\times \sqrt[5]{x^4}$

Using exponent property for radicals $\sqrt[n]{a^m}=a^{\frac{m}{n}}$, we can rewrite our expression as:

$x^{\frac{4}{5}}\times x^{\frac{4}{5}}$

Using exponent property $a^m*a^n=a^{m+n}$, we can rewrite our expression as:

$x^{\frac{4}{5}+\frac{4}{5}}$

$x^{\frac{4+4}{5}}$

$x^{\frac{8}{5}}$

Therefore, the simplified form of our given expression would be $x^{\frac{8}{5}}$.

Answer 2

I believe the following is your problem (if not do rectify me). If so, then:

⁵√x⁴ .⁵√x⁴
1st method: 
⁵√x⁴ .⁵√x⁴ = x⁴/⁵ . x⁴/⁵ = x⁽⁴/⁵ +x⁴/⁵⁾ = x⁸/⁵ = ⁵√x⁸ = ⁵√(x⁵.x³) = x. ⁵√x³
2nd method:
⁵√x⁴ . ⁵√x⁴ = ⁵√(x⁴. x⁴) = ⁵√(x⁴⁺⁴) = ⁵√x⁸ = x .⁵√x³