Basic Math Examples

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

Step 1

Subtract $1$ from $3$ .

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

Step 2

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

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

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 $\frac{2 w^{3}}{u^{2}}$ .

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

Step 3.2

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

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

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

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

$\frac{8 {(w^{3})}^{3}}{{(u^{2})}^{3}} (u w^{3})$

Step 4.2

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

Tap for more steps...

Step 4.2.1

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

$\frac{8 w^{3 \cdot 3}}{{(u^{2})}^{3}} (u w^{3})$

Step 4.2.2

Multiply $3$ by $3$ .

$\frac{8 w^{9}}{{(u^{2})}^{3}} (u w^{3})$

Step 5

Simplify terms.

Tap for more steps...

Step 5.1

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

Tap for more steps...

Step 5.1.1

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

$\frac{8 w^{9}}{u^{2 \cdot 3}} (u w^{3})$

Step 5.1.2

Multiply $2$ by $3$ .

$\frac{8 w^{9}}{u^{6}} (u w^{3})$

Step 5.2

Cancel the common factor of $u$ .

Tap for more steps...

Step 5.2.1

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

$\frac{8 w^{9}}{u \cdot u^{5}} (u w^{3})$

Step 5.2.2

Factor $u$ out of $u w^{3}$ .

$\frac{8 w^{9}}{u \cdot u^{5}} (u (w^{3}))$

Step 5.2.3

Cancel the common factor.

$\frac{8 w^{9}}{u \cdot u^{5}} (u w^{3})$

Step 5.2.4

Rewrite the expression.

$\frac{8 w^{9}}{u^{5}} w^{3}$

Step 5.3

Combine $\frac{8 w^{9}}{u^{5}}$ and $w^{3}$ .

$\frac{8 w^{9} w^{3}}{u^{5}}$

Step 6

Multiply $w^{9}$ by $w^{3}$ by adding the exponents.

Tap for more steps...

Step 6.1

Move $w^{3}$ .

$\frac{8 (w^{3} w^{9})}{u^{5}}$

Step 6.2

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

$\frac{8 w^{3 + 9}}{u^{5}}$

Step 6.3

Add $3$ and $9$ .

$\frac{8 w^{12}}{u^{5}}$