Algebra Examples

${(x \frac{2}{5} y \frac{4}{10})}^{- 5}$

Step 1

Combine $x$ and $\frac{2}{5}$ .

${(\frac{x \cdot 2}{5} \cdot (y (\frac{4}{10})))}^{- 5}$

Step 2

Rewrite using the commutative property of multiplication.

${(\frac{4}{10} \cdot \frac{x \cdot 2}{5} y)}^{- 5}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $10$ .

${(\frac{4}{2 (5)} \cdot \frac{x \cdot 2}{5} y)}^{- 5}$

Step 3.2

Factor $2$ out of $x \cdot 2$ .

${(\frac{4}{2 (5)} \cdot \frac{2 \cdot x}{5} y)}^{- 5}$

Step 3.3

Cancel the common factor.

${(\frac{4}{2 \cdot 5} \cdot \frac{2 \cdot x}{5} y)}^{- 5}$

Step 3.4

Rewrite the expression.

${(\frac{4}{5} \cdot \frac{x}{5} y)}^{- 5}$

Step 4

Multiply $\frac{4}{5}$ by $\frac{x}{5}$ .

${(\frac{4 x}{5 \cdot 5} y)}^{- 5}$

Step 5

Multiply $5$ by $5$ .

${(\frac{4 x}{25} y)}^{- 5}$

Step 6

Combine $\frac{4 x}{25}$ and $y$ .

${(\frac{4 x y}{25})}^{- 5}$

Step 7

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

${(\frac{25}{4 x y})}^{5}$

Step 8

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

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Step 8.1

Apply the product rule to $\frac{25}{4 x y}$ .

$\frac{25^{5}}{{(4 x y)}^{5}}$

Step 8.2

Apply the product rule to $4 x y$ .

$\frac{25^{5}}{{(4 x)}^{5} y^{5}}$

Step 8.3

Apply the product rule to $4 x$ .

$\frac{25^{5}}{4^{5} x^{5} y^{5}}$

Step 9

Raise $25$ to the power of $5$ .

$\frac{9765625}{4^{5} x^{5} y^{5}}$

Step 10

Raise $4$ to the power of $5$ .

$\frac{9765625}{1024 x^{5} y^{5}}$