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

`\bf \sqrt[5]{x^4}\cdot \sqrt[5]{x^4}\implies \sqrt[5]{x^4\cdot x^4}\implies \sqrt[5]{x^(4+4)}\implies \sqrt[5]{x^8}\implies \sqrt[5]{x^(5+3)} \\\\\\ \sqrt[5]{x^5\cdot x^3}\implies x\sqrt[5]{x^3}`

Answer 2

The simplified form will be:
`x\sqrt[5]{x^3}`

Explanation:

The given expression is:
`\sqrt[5]{x^4}*\sqrt[5]{x^4}`

Simplifying the above expression......

`\sqrt[5]{x^4}*\sqrt[5]{x^4}\\ \\ =\sqrt[5]{x^4*x^4}\\ \\ =\sqrt[5]{x^4^+^4}\ [Exponents\ gets\ added\ while\ multiplication]\\ \\ =\sqrt[5]{x^8}\\ \\ =\sqrt[5]{x^5*x^3}\ [As\ 5+3=8] \\ \\ =\sqrt[5]{x^5}*\sqrt[5]{x^3}\\ \\ =x\sqrt[5]{x^3}`

So, the simplified form will be:
`x\sqrt[5]{x^3}`