Calculus Examples

$10 {(- \frac{3}{20})}^{2}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $- \frac{3}{20}$ .

$10 ({(- 1)}^{2} {(\frac{3}{20})}^{2})$

Step 1.2

Apply the product rule to $\frac{3}{20}$ .

$10 ({(- 1)}^{2} \frac{3^{2}}{20^{2}})$

$10 ({(- 1)}^{2} \frac{3^{2}}{20^{2}})$

Step 2

Simplify the expression.

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Step 2.1

Raise $- 1$ to the power of $2$ .

$10 (1 \frac{3^{2}}{20^{2}})$

Step 2.2

Multiply $\frac{3^{2}}{20^{2}}$ by $1$ .

$10 \frac{3^{2}}{20^{2}}$

Step 2.3

Raise $3$ to the power of $2$ .

$10 \frac{9}{20^{2}}$

Step 2.4

Raise $20$ to the power of $2$ .

$10 (\frac{9}{400})$

$10 (\frac{9}{400})$

Step 3

Cancel the common factor of $10$ .

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Step 3.1

Factor $10$ out of $400$ .

$10 \frac{9}{10 (40)}$

Step 3.2

Cancel the common factor.

$10 \frac{9}{10 \cdot 40}$

Step 3.3

Rewrite the expression.

$\frac{9}{40}$

$\frac{9}{40}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{40}$

Decimal Form:

$0.225$

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