Algebra Examples

$\frac{{(2 x)}^{- 2} y^{2}}{{(8 x)}^{- 1} y z^{0}}$

Step 1

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 1.1

Move ${(2 x)}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{y^{2}}{{(8 x)}^{- 1} y z^{0} {(2 x)}^{2}}$

Step 1.2

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

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

Step 1.3

Cancel the common factor of $y^{2}$ and $y$ .

Tap for more steps...

Step 1.3.1

Factor $y$ out of $y^{2} (8 x)$ .

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

Step 1.3.2

Cancel the common factors.

Tap for more steps...

Step 1.3.2.1

Factor $y$ out of $y {(2 x)}^{2}$ .

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

Step 1.3.2.2

Cancel the common factor.

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

Step 1.3.2.3

Rewrite the expression.

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

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $2 x$ .

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

Step 2.2

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

$\frac{y \cdot 8 x}{4 x^{2}}$

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

Cancel the common factor of $8$ and $4$ .

Tap for more steps...

Step 3.1.1

Factor $4$ out of $y \cdot 8 x$ .

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

Step 3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.1.2.1

Factor $4$ out of $4 x^{2}$ .

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

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

$\frac{y \cdot 2 x}{x^{2}}$

Step 3.2

Cancel the common factor of $x$ and $x^{2}$ .

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

Cancel the common factors.

Tap for more steps...

Step 3.2.2.1

Factor $x$ out of $x^{2}$ .

$\frac{x (y \cdot 2)}{x \cdot x}$

Step 3.2.2.2

Cancel the common factor.

$\frac{x (y \cdot 2)}{x \cdot x}$

Step 3.2.2.3

Rewrite the expression.

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

Step 3.3

Move $2$ to the left of $y$ .

$\frac{2 y}{x}$