Question

Rewrite the radical expression as an expression with a rational exponent. the seventh root of x to the third power

Answer 1

Answer:

yes, x to the 3/7th power is correct

Step-by-step explanation:

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Answer 2

The expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths power ⇒ answer A

Step-by-step explanation:

Let us explain how to change the radical expression as an expression

with a rational exponent

1. Find the number of the root and make it the denominator of the

  fraction exponent

2. Find the power of the term under the radical and make it the

   numerator of the fraction exponent

Examples:

$\sqrt{x^{n}}=x^{\frac{n}{2}}$

$\sqrt[3]{x^{n}}=x^{\frac{n}{3}}$

$\sqrt[5]{x^{n}}=x^{\frac{n}{5}}$

So $\sqrt[m]{x^{n}}=x^{\frac{n}{m}}$

∵ the radical expression is the seventh root of x to the third power

∵ seventh root = $\sqrt[7]{}$

∵ x to the third power = x³

∴ seventh root of x to the third power = $\sqrt[7]{x^{3}}$

Let us change it to the rational exponent

∵ $\sqrt[m]{x^{n}}=x^{\frac{n}{m}}$

∵ $\sqrt[7]{x^{3}}$

∴ m = 7 and n = 3

∴ $\sqrt[7]{x^{3}}$ = $x^{\frac{3}{7}}$

∵ $x^{\frac{3}{7}}$ is x to the three sevenths power

∴ $\sqrt[7]{x^{3}}$ is x to the three sevenths power

The expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths power

Learn more:

You can learn more about radical equation is brainly.com/question/7153188

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