Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 4.1

Apply the product rule to $\frac{w}{3 y^{3}}$ .

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

Step 4.2

Apply the product rule to $3 y^{3}$ .

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

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

Raise $3$ to the power of $2$ .

$\frac{w^{2}}{9 {(y^{3})}^{2}}$

Step 5.2

Multiply the exponents in ${(y^{3})}^{2}$ .

Tap for more steps...

Step 5.2.1

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

$\frac{w^{2}}{9 y^{3 \cdot 2}}$

Step 5.2.2

Multiply $3$ by $2$ .

$\frac{w^{2}}{9 y^{6}}$