# 29.5 to the power 2/3?

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Connie Share
Nov 19, 2017

${29.5}^{\frac{2}{3}}$. Okay.

#### Explanation:

Fractional exponents are another way of writing a number that is under a radical and raised to a power.

${29.5}^{\frac{2}{3}}$ is the same as the cube root of 29.5 squared:

${\sqrt[3]{29.5}}^{2}$.

With a fractional exponent, the denominator of the fraction is the root, and the numerator is the power.

${x}^{\frac{1}{2}}$ is the same as $\sqrt{x}$; $\sqrt[3]{x}$ is the same as ${x}^{\frac{1}{3}}$.

In some expressions or equations, you can't work with radical signs, so you use fractional exponents instead.

For this one, if you need a value, use your calculator. You can do either operation first:

square $29.5$ and then take the cube root of that, or

take the cube root of $29.5$ and then square that, or

enter into your calculator: 29.5 ^ (2/3). Either way, you should get a non-repeating, non-terminating decimal:

$9.547317028 \ldots \ldots .$ is what my calculator says.

PS, if your calculator doesn't have a cube root or an nth root button, use the caret $^$ followed by the fraction $\frac{1}{3}$ in parentheses.

Connie

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