Basic Math Examples

$\frac{- 2 {(A y)}^{2}}{2^{3} A^{2} y^{- 3}}$

Step 1

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 1.1

Move $y^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 2 {(A y)}^{2} y^{3}}{2^{3} A^{2}}$

Step 1.2

Cancel the common factor of $- 2$ and $2^{3}$ .

Tap for more steps...

Step 1.2.1

Rewrite $- 2$ as $- 1 (2)$ .

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

Step 1.2.2

Factor $2$ out of $- 1 (2) {(A y)}^{2} y^{3}$ .

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

Step 1.2.3

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1

Factor $2$ out of $2^{3} A^{2}$ .

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

Step 1.2.3.2

Cancel the common factor.

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

Step 1.2.3.3

Rewrite the expression.

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

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Apply the product rule to $A y$ .

$\frac{- 1 A^{2} y^{2} y^{3}}{2^{2} A^{2}}$

Step 2.2

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

Tap for more steps...

Step 2.2.1

Move $y^{3}$ .

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

Step 2.2.2

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

$\frac{- 1 A^{2} y^{3 + 2}}{2^{2} A^{2}}$

Step 2.2.3

Add $3$ and $2$ .

$\frac{- 1 A^{2} y^{5}}{2^{2} A^{2}}$

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

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

$\frac{- 1 A^{2} y^{5}}{4 A^{2}}$

Step 3.2

Cancel the common factor of $A^{2}$ .

Tap for more steps...

Step 3.2.1

Cancel the common factor.

$\frac{- 1 A^{2} y^{5}}{4 A^{2}}$

Step 3.2.2

Rewrite the expression.

$\frac{- 1 y^{5}}{4}$

Step 3.3

Move the negative in front of the fraction.

$- \frac{y^{5}}{4}$