Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

Tap for more steps...

Step 3.1

Apply the product rule to $\frac{u w^{2}}{3 v^{2}}$ .

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

Step 3.2

Apply the product rule to $u w^{2}$ .

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

Step 3.3

Apply the product rule to $3 v^{2}$ .

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

Step 4

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

Tap for more steps...

Step 4.1

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

$\frac{u^{3} w^{2 \cdot 3}}{3^{3} {(v^{2})}^{3}} (u^{3} w^{- 1})$

Step 4.2

Multiply $2$ by $3$ .

$\frac{u^{3} w^{6}}{3^{3} {(v^{2})}^{3}} (u^{3} w^{- 1})$

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

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

$\frac{u^{3} w^{6}}{27 {(v^{2})}^{3}} (u^{3} w^{- 1})$

Step 5.2

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

Tap for more steps...

Step 5.2.1

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

$\frac{u^{3} w^{6}}{27 v^{2 \cdot 3}} (u^{3} w^{- 1})$

Step 5.2.2

Multiply $2$ by $3$ .

$\frac{u^{3} w^{6}}{27 v^{6}} (u^{3} w^{- 1})$

Step 6

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

$\frac{u^{3} w^{6}}{27 v^{6}} (u^{3} \frac{1}{w})$

Step 7

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

$\frac{u^{3} w^{6}}{27 v^{6}} \cdot \frac{u^{3}}{w}$

Step 8

Combine.

$\frac{u^{3} w^{6} u^{3}}{27 v^{6} w}$

Step 9

Multiply $u^{3}$ by $u^{3}$ by adding the exponents.

Tap for more steps...

Step 9.1

Move $u^{3}$ .

$\frac{u^{3} u^{3} w^{6}}{27 v^{6} w}$

Step 9.2

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

$\frac{u^{3 + 3} w^{6}}{27 v^{6} w}$

Step 9.3

Add $3$ and $3$ .

$\frac{u^{6} w^{6}}{27 v^{6} w}$

Step 10

Cancel the common factor of $w^{6}$ and $w$ .

Tap for more steps...

Step 10.1

Factor $w$ out of $u^{6} w^{6}$ .

$\frac{w (u^{6} w^{5})}{27 v^{6} w}$

Step 10.2

Cancel the common factors.

Tap for more steps...

Step 10.2.1

Factor $w$ out of $27 v^{6} w$ .

$\frac{w (u^{6} w^{5})}{w (27 v^{6})}$

Step 10.2.2

Cancel the common factor.

$\frac{w (u^{6} w^{5})}{w (27 v^{6})}$

Step 10.2.3

Rewrite the expression.

$\frac{u^{6} w^{5}}{27 v^{6}}$