Precalculus Examples

$\frac{75}{400^{2}} \cdot {(200)}^{2}$

Step 1

Raise $400$ to the power of $2$ .

$\frac{75}{160000} \cdot {(200)}^{2}$

Step 2

Cancel the common factor of $75$ and $160000$ .

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Step 2.1

Factor $25$ out of $75$ .

$\frac{25 (3)}{160000} \cdot {(200)}^{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $25$ out of $160000$ .

$\frac{25 \cdot 3}{25 \cdot 6400} \cdot {(200)}^{2}$

Step 2.2.2

Cancel the common factor.

$\frac{25 \cdot 3}{25 \cdot 6400} \cdot {(200)}^{2}$

Step 2.2.3

Rewrite the expression.

$\frac{3}{6400} \cdot {(200)}^{2}$

Step 3

Raise $200$ to the power of $2$ .

$\frac{3}{6400} \cdot 40000$

Step 4

Cancel the common factor of $1600$ .

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Step 4.1

Factor $1600$ out of $6400$ .

$\frac{3}{1600 (4)} \cdot 40000$

Step 4.2

Factor $1600$ out of $40000$ .

$\frac{3}{1600 \cdot 4} \cdot (1600 \cdot 25)$

Step 4.3

Cancel the common factor.

$\frac{3}{1600 \cdot 4} \cdot (1600 \cdot 25)$

Step 4.4

Rewrite the expression.

$\frac{3}{4} \cdot 25$

Step 5

Combine $\frac{3}{4}$ and $25$ .

$\frac{3 \cdot 25}{4}$

Step 6

Multiply $3$ by $25$ .

$\frac{75}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{75}{4}$

Decimal Form:

$18.75$

Mixed Number Form:

$18 \frac{3}{4}$