Basic Math Examples

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

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 $- \frac{2}{5}$ .

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

Step 1.2

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

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

Step 2

Evaluate the exponents.

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Step 2.1

Raise $- 1$ to the power of $5$ .

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

Step 2.2

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

$- \frac{32}{5^{5}} \cdot \frac{1}{2}$

Step 2.3

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

$- \frac{32}{3125} \cdot \frac{1}{2}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Move the leading negative in $- \frac{32}{3125}$ into the numerator.

$\frac{- 32}{3125} \cdot \frac{1}{2}$

Step 3.2

Factor $2$ out of $- 32$ .

$\frac{2 (- 16)}{3125} \cdot \frac{1}{2}$

Step 3.3

Cancel the common factor.

$\frac{2 \cdot - 16}{3125} \cdot \frac{1}{2}$

Step 3.4

Rewrite the expression.

$\frac{- 16}{3125}$

Step 4

Move the negative in front of the fraction.

$- \frac{16}{3125}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{16}{3125}$

Decimal Form:

$- 0.00512$