Algebra Examples

${(a^{3} b)}^{- 2} (a^{3} b^{4})$

Step 1

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

$\frac{1}{{(a^{3} b)}^{2}} (a^{3} b^{4})$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $a^{3} b$ .

$\frac{1}{{(a^{3})}^{2} b^{2}} (a^{3} b^{4})$

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

$\frac{1}{a^{3 \cdot 2} b^{2}} (a^{3} b^{4})$

Step 2.2.2

Multiply $3$ by $2$ .

$\frac{1}{a^{6} b^{2}} (a^{3} b^{4})$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Cancel the common factor of $a^{3} b^{2}$ .

Tap for more steps...

Step 3.1.1

Factor $a^{3} b^{2}$ out of $a^{6} b^{2}$ .

$\frac{1}{a^{3} b^{2} (a^{3})} (a^{3} b^{4})$

Step 3.1.2

Factor $a^{3} b^{2}$ out of $a^{3} b^{4}$ .

$\frac{1}{a^{3} b^{2} (a^{3})} (a^{3} b^{2} (b^{2}))$

Step 3.1.3

Cancel the common factor.

$\frac{1}{a^{3} b^{2} a^{3}} (a^{3} b^{2} b^{2})$

Step 3.1.4

Rewrite the expression.

$\frac{1}{a^{3}} b^{2}$

Step 3.2

Combine $\frac{1}{a^{3}}$ and $b^{2}$ .

$\frac{b^{2}}{a^{3}}$