Basic Math Examples

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

Step 1

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

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

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $w^{- 1} y$ .

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

Step 2.2

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

Tap for more steps...

Step 2.2.1

Move $y^{2}$ .

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

Step 2.2.2

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

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

Step 2.2.3

Add $2$ and $3$ .

$\frac{3 w}{{(w^{- 1})}^{3} y^{5}}$

Step 2.3

Multiply the exponents in ${(w^{- 1})}^{3}$ .

Tap for more steps...

Step 2.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3 w}{w^{- 1 \cdot 3} y^{5}}$

Step 2.3.2

Multiply $- 1$ by $3$ .

$\frac{3 w}{w^{- 3} y^{5}}$

Step 2.4

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

$\frac{3 w}{\frac{1}{w^{3}} y^{5}}$

Step 3

Combine $\frac{1}{w^{3}}$ and $y^{5}$ .

$\frac{3 w}{\frac{y^{5}}{w^{3}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$3 w \frac{w^{3}}{y^{5}}$

Step 5

Multiply $3 w \frac{w^{3}}{y^{5}}$ .

Tap for more steps...

Step 5.1

Combine $3$ and $\frac{w^{3}}{y^{5}}$ .

$w \frac{3 w^{3}}{y^{5}}$

Step 5.2

Combine $w$ and $\frac{3 w^{3}}{y^{5}}$ .

$\frac{w (3 w^{3})}{y^{5}}$

Step 5.3

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

$\frac{3 (w^{1} w^{3})}{y^{5}}$

Step 5.4

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

$\frac{3 w^{1 + 3}}{y^{5}}$

Step 5.5

Add $1$ and $3$ .

$\frac{3 w^{4}}{y^{5}}$