Respuesta :

SaniShahbaz

Answer:

[tex]x^\frac{21}{5}[/tex]

Step-by-step explanation:

We are given an expression and we have to transform it into an expression with exponent.

5th root of x can be written as [tex]x^\frac{1}{5}[/tex]

[tex](\sqrt[5]{x^7})^3\\\\((x^7)^\frac{1}{5} )^3[/tex]


The powers outside will be multiplied as: [tex](x^a)^b = x^{ab}[/tex]

[tex](x^\frac{7}{5} )^3\\x^\frac{7*3}{5}\\x^\frac{21}{5}[/tex]


where the exponent is [tex]\frac{21}{5}[/tex] and it is a rational number by definition of rational numbers

abidemiokin

The required rational exponent of the expression is [tex]x^{\frac{21}{5} }[/tex]

Indices are expressions written  using exponents

According to the law of indices

[tex](a^m)^n = a^{mn}\\(\sqrt[a]{m})^n=m^{\frac{n}{a} }[/tex]

Given the indicinal expression

[tex](\sqrt[5]{x^7})^3[/tex]

This can also be expressed as:

[tex]\sqrt[5]{x^7} =(x^7)^{\frac{1}{5 }[/tex]

[tex]=(\sqrt[5]{x^7} )^3\\=(x^{\frac{7}{5} })^3\\=x^{\frac{21}{5} }[/tex]

Hence the required rational exponent of the expression is [tex]x^{\frac{21}{5} }[/tex]

Learn more here: https://brainly.com/question/16933066

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