Answer:
[tex]x^{\frac{8}{5}}[/tex].
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:
[tex]\sqrt[5]{x^4}\times \sqrt[5]{x^4}[/tex]
Using exponent property for radicals [tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex], we can rewrite our expression as:
[tex]x^{\frac{4}{5}}\times x^{\frac{4}{5}}[/tex]
Using exponent property [tex]a^m*a^n=a^{m+n}[/tex], we can rewrite our expression as:
[tex]x^{\frac{4}{5}+\frac{4}{5}}[/tex]
[tex]x^{\frac{4+4}{5}}[/tex]
[tex]x^{\frac{8}{5}}[/tex]
Therefore, the simplified form of our given expression would be [tex]x^{\frac{8}{5}}[/tex].
