Algebra Examples

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

Step 1

Move ${(8 x^{- 3} y)}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Multiply $x^{2}$ by $x^{- 3}$ by adding the exponents.

Tap for more steps...

Step 2.1.1

Move $x^{- 3}$ .

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

Step 2.1.2

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

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

Step 2.1.3

Add $- 3$ and $2$ .

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

Step 2.2

Multiply $y^{- 1}$ by $y$ by adding the exponents.

Tap for more steps...

Step 2.2.1

Move $y$ .

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

Step 2.2.2

Multiply $y$ by $y^{- 1}$ .

Tap for more steps...

Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.3

Subtract $1$ from $1$ .

$\frac{1}{2 x^{- 1} y^{0} \cdot 8}$

Step 2.3

Simplify $2 x^{- 1} y^{0} \cdot 8$ .

$\frac{1}{2 x^{- 1} \cdot 8}$

Step 3

Move $x^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{x}{2 \cdot 8}$

Step 4

Multiply $2$ by $8$ .

$\frac{x}{16}$