Algebra Examples

$\frac{1}{6} {(\frac{4}{5})}^{- 2}$

Step 1

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

$\frac{1}{6} \cdot {(\frac{5}{4})}^{2}$

Step 2

Apply the product rule to $\frac{5}{4}$ .

$\frac{1}{6} \cdot \frac{5^{2}}{4^{2}}$

Step 3

Combine.

$\frac{1 \cdot 5^{2}}{6 \cdot 4^{2}}$

Step 4

Simplify the expression.

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Step 4.1

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

$\frac{5^{2}}{6 \cdot 4^{2}}$

Step 4.2

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

$\frac{5^{2}}{6 \cdot 16}$

Step 4.3

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

$\frac{25}{6 \cdot 16}$

Step 4.4

Multiply $6$ by $16$ .

$\frac{25}{96}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{96}$

Decimal Form:

$0.26041\overline{6}$