# How do you evaluate and simplify 25^(3/2)?

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14
Jan 25, 2017

${25}^{\frac{3}{2}} = 125$

#### Explanation:

For any Real numbers $a$, $b$, $c$ with $a > 0$ we find:

${a}^{b c} = {\left({a}^{b}\right)}^{c}$

In our example, $25 = {5}^{2}$, so we find:

${25}^{\frac{3}{2}} = {\left({5}^{2}\right)}^{\frac{3}{2}} = {5}^{2 \cdot \frac{3}{2}} = {5}^{3} = 125$

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Frit L. Share
Jan 25, 2017

the answer is 125.

#### Explanation:

to the power of 1/2 means that the number is being square rooted. So to the power of 3/2 that means the number is being cubed and then square rooted. 25 cubed is 15625. 15625 square rooted is 125.

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