Question

Rewrite The following expression.

Answer 1

Choice A is correct

Explanation:

We have been given the expression;

`x^{(9)/(7) }`

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

`a^{(b)/(c) }=(a^(b))^{(1)/(c) }`

Using this law, the expression can be written as;

`(x^(9))^{(1)/(7)}`

The next thing we need to remember is that;

`a^{(1)/(n) }=\sqrt[n]{a}`

Therefore, the expression becomes;

`\sqrt[7]{x^(9) }`

Next,

`x^(9)=x^(7)*x^(2)`

This implies that;

`\sqrt[7]{x^(9) }=\sqrt[7]{x^(7)*x^(2)}\\=\sqrt[7]{x^(7) }*\sqrt[7]{x^(2) } \\=x\sqrt[7]{x^(2) }`

Answer 2

A.

`x \sqrt[7]{{x}^(2) } .`

EXPLANATION

The given expression is

`{x}^{ (9)/(7) }`

We want to rewrite the given expression in radical form:

Recall that:

`{a}^{ (m)/(n) } = \sqrt[n]{ {a}^(m) }`

This implies that:

`{x}^{ (9)/(7) } = \sqrt[7]{ {x}^(9) }`

`{x}^{ (9)/(7) } = \sqrt[7]{ {x}^(7) * {x}^(2) }`

Split the radicals.

`{x}^{ (9)/(7) } = \sqrt[7]{ {x}^(7) } * \sqrt[7]{{x}^(2) }`

This finally simplifies to:

`{x}^{ (9)/(7) }=x \sqrt[7]{{x}^(2) }`

The correct answer is A.