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

`x^{(8)/(5)}`.

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}* \sqrt[5]{x^4}`

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

`x^{(4)/(5)}* x^{(4)/(5)}`

Using exponent property
`a^m*a^n=a^(m+n)`, we can rewrite our expression as:

`x^{(4)/(5)+(4)/(5)}`

`x^{(4+4)/(5)}`

`x^{(8)/(5)}`

Therefore, the simplified form of our given expression would be
`x^{(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