QuestionCalculate $25^{\frac{3}{2}}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression $25^{\frac{3}{}}$ .

STEP 2

The expression $25^{\frac{}{2}}$ can be broken down into two parts $25^{\frac{1}{2}}$ and $25^{\frac{2}{2}}$ .

STEP 3

First, let's calculate $25^{\frac{1}{2}}$ . The exponent of $\frac{1}{2}$ is equivalent to taking the square root.
$25^{\frac{1}{2}} = \sqrt{25}$

STEP 4

Calculate the square root of25.
$\sqrt{25} =$

STEP 5

Now, let's calculate $25^{\frac{2}{2}}$ . The exponent of $\frac{2}{2}$ is equivalent to taking the square root and then squaring the result.
$25^{\frac{2}{2}} = (25^{\frac{1}{2}})^2$

STEP 6

Substitute the result from4 into the equation.
$(25^{\frac{1}{2}})^2 =5^2$

STEP 7

Calculate the square of5.
$5^2 =25$

STEP 8

Now, let's calculate $25^{\frac{3}{2}}$ . This is equivalent to multiplying $25^{\frac{1}{2}}$ by $25^{\frac{2}{2}}$ .
$25^{\frac{3}{2}} =25^{\frac{1}{2}} \times25^{\frac{2}{2}}$

STEP 9

Substitute the results from4 and7 into the equation.
$25^{\frac{3}{2}} =5 \times25$

STEP 10

Calculate the product of5 and25.
$5 \times25 =125$ So, $25^{\frac{3}{2}} =125$ .

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