Precalculus Examples

$(2 u^{2} v^{3}) {(3 u^{3} v)}^{- 2}$

Step 1

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

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

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

$2 u^{2} v^{3} \frac{1}{9 {(u^{3})}^{2} v^{2}}$

Step 2.4

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

Tap for more steps...

Step 2.4.1

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

$2 u^{2} v^{3} \frac{1}{9 u^{3 \cdot 2} v^{2}}$

Step 2.4.2

Multiply $3$ by $2$ .

$2 u^{2} v^{3} \frac{1}{9 u^{6} v^{2}}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Cancel the common factor of $u^{2} v^{2}$ .

Tap for more steps...

Step 3.1.1

Factor $u^{2} v^{2}$ out of $2 u^{2} v^{3}$ .

$u^{2} v^{2} (2 v) \frac{1}{9 u^{6} v^{2}}$

Step 3.1.2

Factor $u^{2} v^{2}$ out of $9 u^{6} v^{2}$ .

$u^{2} v^{2} (2 v) \frac{1}{u^{2} v^{2} (9 u^{4})}$

Step 3.1.3

Cancel the common factor.

$u^{2} v^{2} (2 v) \frac{1}{u^{2} v^{2} (9 u^{4})}$

Step 3.1.4

Rewrite the expression.

$2 v \frac{1}{9 u^{4}}$

Step 3.2

Combine $2$ and $\frac{1}{9 u^{4}}$ .

$v \frac{2}{9 u^{4}}$

Step 3.3

Combine $v$ and $\frac{2}{9 u^{4}}$ .

$\frac{v \cdot 2}{9 u^{4}}$

Step 3.4

Move $2$ to the left of $v$ .

$\frac{2 v}{9 u^{4}}$