Question

Rewrite the expression with rational exponents as a radical expression.

7 times x to the two thirds power

9 times the cube root of x to the power of 2
7 times the square root of x to the power of 3
cube root of the quantity 9 times x to the power of 2
square root of the quantity 9 times x to the power of 3

Answer 1

To rewrite the expression with rational exponents as a radical expression, we look at the given term:

**7 times x to the two thirds power**

This can be expressed as:

\[
7 \times x^{\frac{2}{3}}
\]

Using the properties of exponents, we can rewrite this as:

\[
7 \times \frac{x^2}{\sqrt[3]{x}}
\]

However, it's more common to express \( x^{\frac{2}{3}} \) using radicals:

\[
7 \times \sqrt[3]{x^2}
\]

Thus, the rewritten expression with rational exponents as a radical expression is:

**7 times the cube root of x squared (7√[3]{x²})**.

In the context of your options, this corresponds to:

**cube root of the quantity 9 times x to the power of 2** (if considering the "9" as part of a different expression).

So, the answer fits with this understanding, but if we specifically stay with just the rational exponent given, the boxed answer is:

**7 times the cube root of x squared (7√[3]{x²})**.