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:

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

Step-by-step 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:  $x\sqrt[5]{x^3}$

Answer 2

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