Respuesta :

Answer:

Choice A is correct

Step-by-step explanation:

We have been given the expression;

[tex]x^{\frac{9}{7} }[/tex]

In order to re-write this expression, we shall use some laws of exponents;

[tex]a^{\frac{b}{c} }=(a^{b})^{\frac{1}{c} }[/tex]

Using this law, the expression can be written as;

[tex](x^{9})^{\frac{1}{7}}[/tex]

The next thing we need to remember is that;

[tex]a^{\frac{1}{n} }=\sqrt[n]{a}[/tex]

Therefore, the expression becomes;

[tex]\sqrt[7]{x^{9} }[/tex]

Next,

[tex]x^{9}=x^{7}*x^{2}[/tex]

This implies that;

[tex]\sqrt[7]{x^{9} }=\sqrt[7]{x^{7}*x^{2}}\\=\sqrt[7]{x^{7} }*\sqrt[7]{x^{2} } \\=x\sqrt[7]{x^{2} }[/tex]

kudzordzifrancis

ANSWER

A.

[tex]x \sqrt[7]{{x}^{2} } .[/tex]

EXPLANATION

The given expression is

[tex] {x}^{ \frac{9}{7} } [/tex]

We want to rewrite the given expression in radical form:

Recall that:

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

This implies that:

[tex] {x}^{ \frac{9}{7} } = \sqrt[7]{ {x}^{9} } [/tex]

[tex]{x}^{ \frac{9}{7} } = \sqrt[7]{ {x}^{7} \times {x}^{2} } [/tex]

Split the radicals.

[tex]{x}^{ \frac{9}{7} } = \sqrt[7]{ {x}^{7} } \times \sqrt[7]{{x}^{2} } [/tex]

This finally simplifies to:

[tex]{x}^{ \frac{9}{7} }=x \sqrt[7]{{x}^{2} } [/tex]

The correct answer is A.

Otras preguntas