Basic Math Examples

${(- \frac{5}{1})}^{3} {(- \frac{1}{5})}^{2}$

Step 1

Divide $5$ by $1$ .

${(- 1 \cdot 5)}^{3} {(- \frac{1}{5})}^{2}$

Step 2

Multiply $- 1$ by $5$ .

${(- 5)}^{3} {(- \frac{1}{5})}^{2}$

Step 3

Raise $- 5$ to the power of $3$ .

$- 125 {(- \frac{1}{5})}^{2}$

Step 4

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

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Step 4.1

Apply the product rule to $- \frac{1}{5}$ .

$- 125 ({(- 1)}^{2} {(\frac{1}{5})}^{2})$

Step 4.2

Apply the product rule to $\frac{1}{5}$ .

$- 125 ({(- 1)}^{2} \frac{1^{2}}{5^{2}})$

$- 125 ({(- 1)}^{2} \frac{1^{2}}{5^{2}})$

Step 5

Simplify the expression.

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Step 5.1

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

$- 125 (1 \frac{1^{2}}{5^{2}})$

Step 5.2

Multiply $\frac{1^{2}}{5^{2}}$ by $1$ .

$- 125 \frac{1^{2}}{5^{2}}$

Step 5.3

One to any power is one.

$- 125 \frac{1}{5^{2}}$

Step 5.4

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

$- 125 (\frac{1}{25})$

$- 125 (\frac{1}{25})$

Step 6

Cancel the common factor of $25$ .

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Step 6.1

Factor $25$ out of $- 125$ .

$25 (- 5) \frac{1}{25}$

Step 6.2

Cancel the common factor.

$25 \cdot - 5 \frac{1}{25}$

Step 6.3

Rewrite the expression.

$- 5$

$- 5$

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