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}).
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