Algebra Examples

${(8 x y)}^{- 2} \cdot \frac{x^{- 5} y^{- 1}}{x y}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(8 x y)}^{- 2} \cdot \frac{\frac{1}{x^{5}} y^{- 1}}{x y}$

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(8 x y)}^{- 2} \cdot \frac{\frac{1}{x^{5}} \cdot \frac{1}{y}}{x y}$

Step 2

Multiply $\frac{1}{x^{5}}$ by $\frac{1}{y}$ .

${(8 x y)}^{- 2} \cdot \frac{\frac{1}{x^{5} y}}{x y}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(8 x y)}^{2}} \cdot \frac{\frac{1}{x^{5} y}}{x y}$

Step 4

Combine fractions.

Tap for more steps...

Step 4.1

Combine.

$\frac{1 \frac{1}{x^{5} y}}{{(8 x y)}^{2} (x y)}$

Step 4.2

Multiply $\frac{1}{x^{5} y}$ by $1$ .

$\frac{\frac{1}{x^{5} y}}{{(8 x y)}^{2} x y}$

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

Apply the product rule to $8 x y$ .

$\frac{\frac{1}{x^{5} y}}{{(8 x)}^{2} y^{2} x y}$

Step 5.2

Combine exponents.

Tap for more steps...

Step 5.2.1

Raise $y$ to the power of $1$ .

$\frac{\frac{1}{x^{5} y}}{{(8 x)}^{2} x (y^{2} y^{1})}$

Step 5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\frac{1}{x^{5} y}}{{(8 x)}^{2} x y^{2 + 1}}$

Step 5.2.3

Add $2$ and $1$ .

$\frac{\frac{1}{x^{5} y}}{{(8 x)}^{2} x y^{3}}$

Step 5.3

Apply the product rule to $8 x$ .

$\frac{\frac{1}{x^{5} y}}{8^{2} x^{2} x y^{3}}$

Step 5.4

Raise $8$ to the power of $2$ .

$\frac{\frac{1}{x^{5} y}}{64 x^{2} x y^{3}}$

Step 5.5

Combine exponents.

Tap for more steps...

Step 5.5.1

Raise $x$ to the power of $1$ .

$\frac{\frac{1}{x^{5} y}}{64 (x^{1} x^{2}) y^{3}}$

Step 5.5.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\frac{1}{x^{5} y}}{64 x^{1 + 2} y^{3}}$

Step 5.5.3

Add $1$ and $2$ .

$\frac{\frac{1}{x^{5} y}}{64 x^{3} y^{3}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{x^{5} y} \cdot \frac{1}{64 x^{3} y^{3}}$

Step 7

Combine.

$\frac{1 \cdot 1}{x^{5} y (64 x^{3} y^{3})}$

Step 8

Multiply $x^{5}$ by $x^{3}$ by adding the exponents.

Tap for more steps...

Step 8.1

Move $x^{3}$ .

$\frac{1 \cdot 1}{x^{3} x^{5} y (64 y^{3})}$

Step 8.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1 \cdot 1}{x^{3 + 5} y (64 y^{3})}$

Step 8.3

Add $3$ and $5$ .

$\frac{1 \cdot 1}{x^{8} y (64 y^{3})}$

Step 9

Multiply $y$ by $y^{3}$ by adding the exponents.

Tap for more steps...

Step 9.1

Move $y^{3}$ .

$\frac{1 \cdot 1}{x^{8} (y^{3} y) \cdot 64}$

Step 9.2

Multiply $y^{3}$ by $y$ .

Tap for more steps...

Step 9.2.1

Raise $y$ to the power of $1$ .

$\frac{1 \cdot 1}{x^{8} (y^{3} y^{1}) \cdot 64}$

Step 9.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1 \cdot 1}{x^{8} y^{3 + 1} \cdot 64}$

Step 9.3

Add $3$ and $1$ .

$\frac{1 \cdot 1}{x^{8} y^{4} \cdot 64}$

Step 10

Multiply $1$ by $1$ .

$\frac{1}{x^{8} y^{4} \cdot 64}$

Step 11

Move $64$ to the left of $x^{8} y^{4}$ .

$\frac{1}{64 x^{8} y^{4}}$