andrewfrobins
contestada

Which of the following is the simplified form of fifth root of x times the fifth root of x times the fifth root of x times the fifth root of x?

x to the 1 over fifth power
x to the 4 over fifth power
x to the four over twentieth power
x

Respuesta :

gmany

Answer:

[tex]\large\boxed{x^\frac{4}{5}}[/tex]

Step-by-step explanation:

[tex]\sqrt[n]{a}=a^\frac{1}{n}\Rightarrow\sqrt[5]{x}=x^\frac{1}{5}\\\\\sqrt[5]{x}\cdot\sqrt[5]{x}\cdot\sqrt[5]{x}\cdot\sqrt[5]{x}=x^\frac{1}{5}\cdot x^\frac{1}{5}\cdot x^\frac{1}{5}\cdot x^\frac{1}{5}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=x^{\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}=x^\frac{4}{5}[/tex]

Answer:

[tex]x^{\frac{4}{5}}[/tex]

Step-by-step explanation:

fifth root of x can be written in exponential for as:

[tex]x^\frac{1}{5}[/tex]

[tex]x^\frac{1}{5}[/tex] times  [tex]x^\frac{1}{5}[/tex] times  [tex]x^\frac{1}{5}[/tex] times  [tex]x^\frac{1}{5}[/tex]

WE apply exponential property to multiply it

a^m times a^n= a^{m+n}

[tex]x^\frac{1}{5}[/tex] times  [tex]x^\frac{1}{5}[/tex] times  [tex]x^\frac{1}{5}[/tex] times  [tex]x^\frac{1}{5}[/tex]

[tex]x^{\frac{1}{5} +\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}[/tex]

The denominator of the fractions are same so we add the numerators

[tex]x^{\frac{4}{5}}[/tex]

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