Precalculus Examples

${(\frac{1}{2})}^{4} \cdot {(\frac{5}{2})}^{- 2}$

Step 1

Apply the product rule to $\frac{1}{2}$ .

$\frac{1^{4}}{2^{4}} \cdot {(\frac{5}{2})}^{- 2}$

Step 2

One to any power is one.

$\frac{1}{2^{4}} \cdot {(\frac{5}{2})}^{- 2}$

Step 3

Raise $2$ to the power of $4$ .

$\frac{1}{16} \cdot {(\frac{5}{2})}^{- 2}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{1}{16} \cdot {(\frac{2}{5})}^{2}$

Step 5

Apply the product rule to $\frac{2}{5}$ .

$\frac{1}{16} \cdot \frac{2^{2}}{5^{2}}$

Step 6

Combine.

$\frac{1 \cdot 2^{2}}{16 \cdot 5^{2}}$

Step 7

Simplify the expression.

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Step 7.1

Multiply $2^{2}$ by $1$ .

$\frac{2^{2}}{16 \cdot 5^{2}}$

Step 7.2

Raise $5$ to the power of $2$ .

$\frac{2^{2}}{16 \cdot 25}$

Step 7.3

Raise $2$ to the power of $2$ .

$\frac{4}{16 \cdot 25}$

Step 7.4

Multiply $16$ by $25$ .

$\frac{4}{400}$

$\frac{4}{400}$

Step 8

Cancel the common factor of $4$ and $400$ .

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Step 8.1

Factor $4$ out of $4$ .

$\frac{4 (1)}{400}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $4$ out of $400$ .

$\frac{4 \cdot 1}{4 \cdot 100}$

Step 8.2.2

Cancel the common factor.

$\frac{4 \cdot 1}{4 \cdot 100}$

Step 8.2.3

Rewrite the expression.

$\frac{1}{100}$

$\frac{1}{100}$

$\frac{1}{100}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{100}$

Decimal Form:

$0.01$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$