Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

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

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

Step 1.2

Apply the product rule to $3 b$ .

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

Step 2

Multiply the exponents in ${(a^{3})}^{4}$ .

Tap for more steps...

Step 2.1

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

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

Step 2.2

Multiply $3$ by $4$ .

$\frac{a^{12}}{3^{4} b^{4}} \cdot {(\frac{6 b^{3}}{a^{4}})}^{2}$

Step 3

Raise $3$ to the power of $4$ .

$\frac{a^{12}}{81 b^{4}} \cdot {(\frac{6 b^{3}}{a^{4}})}^{2}$

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 $\frac{6 b^{3}}{a^{4}}$ .

$\frac{a^{12}}{81 b^{4}} \cdot \frac{{(6 b^{3})}^{2}}{{(a^{4})}^{2}}$

Step 4.2

Apply the product rule to $6 b^{3}$ .

$\frac{a^{12}}{81 b^{4}} \cdot \frac{6^{2} {(b^{3})}^{2}}{{(a^{4})}^{2}}$

Step 5

Combine.

$\frac{a^{12} (6^{2} {(b^{3})}^{2})}{81 b^{4} {(a^{4})}^{2}}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Raise $6$ to the power of $2$ .

$\frac{a^{12} \cdot 36 {(b^{3})}^{2}}{81 b^{4} {(a^{4})}^{2}}$

Step 6.2

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

Tap for more steps...

Step 6.2.1

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

$\frac{a^{12} \cdot 36 b^{3 \cdot 2}}{81 b^{4} {(a^{4})}^{2}}$

Step 6.2.2

Multiply $3$ by $2$ .

$\frac{a^{12} \cdot 36 b^{6}}{81 b^{4} {(a^{4})}^{2}}$

Step 7

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 7.1

Multiply the exponents in ${(a^{4})}^{2}$ .

Tap for more steps...

Step 7.1.1

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

$\frac{a^{12} \cdot 36 b^{6}}{81 b^{4} a^{4 \cdot 2}}$

Step 7.1.2

Multiply $4$ by $2$ .

$\frac{a^{12} \cdot 36 b^{6}}{81 b^{4} a^{8}}$

Step 7.2

Cancel the common factor of $a^{12}$ and $a^{8}$ .

Tap for more steps...

Step 7.2.1

Factor $a^{8}$ out of $a^{12} \cdot 36 b^{6}$ .

$\frac{a^{8} (a^{4} \cdot 36 b^{6})}{81 b^{4} a^{8}}$

Step 7.2.2

Cancel the common factors.

Tap for more steps...

Step 7.2.2.1

Factor $a^{8}$ out of $81 b^{4} a^{8}$ .

$\frac{a^{8} (a^{4} \cdot 36 b^{6})}{a^{8} (81 b^{4})}$

Step 7.2.2.2

Cancel the common factor.

$\frac{a^{8} (a^{4} \cdot 36 b^{6})}{a^{8} (81 b^{4})}$

Step 7.2.2.3

Rewrite the expression.

$\frac{a^{4} \cdot 36 b^{6}}{81 b^{4}}$

Step 7.3

Cancel the common factor of $36$ and $81$ .

Tap for more steps...

Step 7.3.1

Factor $9$ out of $a^{4} \cdot 36 b^{6}$ .

$\frac{9 (a^{4} \cdot 4 b^{6})}{81 b^{4}}$

Step 7.3.2

Cancel the common factors.

Tap for more steps...

Step 7.3.2.1

Factor $9$ out of $81 b^{4}$ .

$\frac{9 (a^{4} \cdot 4 b^{6})}{9 (9 b^{4})}$

Step 7.3.2.2

Cancel the common factor.

$\frac{9 (a^{4} \cdot 4 b^{6})}{9 (9 b^{4})}$

Step 7.3.2.3

Rewrite the expression.

$\frac{a^{4} \cdot 4 b^{6}}{9 b^{4}}$

Step 7.4

Cancel the common factor of $b^{6}$ and $b^{4}$ .

Tap for more steps...

Step 7.4.1

Factor $b^{4}$ out of $a^{4} \cdot 4 b^{6}$ .

$\frac{b^{4} (a^{4} \cdot 4 b^{2})}{9 b^{4}}$

Step 7.4.2

Cancel the common factors.

Tap for more steps...

Step 7.4.2.1

Factor $b^{4}$ out of $9 b^{4}$ .

$\frac{b^{4} (a^{4} \cdot 4 b^{2})}{b^{4} \cdot 9}$

Step 7.4.2.2

Cancel the common factor.

$\frac{b^{4} (a^{4} \cdot 4 b^{2})}{b^{4} \cdot 9}$

Step 7.4.2.3

Rewrite the expression.

$\frac{a^{4} \cdot 4 b^{2}}{9}$

Step 7.5

Move $4$ to the left of $a^{4}$ .

$\frac{4 a^{4} b^{2}}{9}$