Algebra Examples

${(\frac{6 a^{2}}{4 b^{4}})}^{2} \cdot \frac{5 b}{3 a}$

Step 1

Cancel the common factor of $6$ and $4$ .

Tap for more steps...

Step 1.1

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

${(\frac{2 (3 a^{2})}{4 b^{4}})}^{2} \cdot \frac{5 b}{3 a}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

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

${(\frac{2 (3 a^{2})}{2 (2 b^{4})})}^{2} \cdot \frac{5 b}{3 a}$

Step 1.2.2

Cancel the common factor.

${(\frac{2 (3 a^{2})}{2 (2 b^{4})})}^{2} \cdot \frac{5 b}{3 a}$

Step 1.2.3

Rewrite the expression.

${(\frac{3 a^{2}}{2 b^{4}})}^{2} \cdot \frac{5 b}{3 a}$

Step 2

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

Tap for more steps...

Step 2.1

Apply the product rule to $\frac{3 a^{2}}{2 b^{4}}$ .

$\frac{{(3 a^{2})}^{2}}{{(2 b^{4})}^{2}} \cdot \frac{5 b}{3 a}$

Step 2.2

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

$\frac{3^{2} {(a^{2})}^{2}}{{(2 b^{4})}^{2}} \cdot \frac{5 b}{3 a}$

Step 2.3

Apply the product rule to $2 b^{4}$ .

$\frac{3^{2} {(a^{2})}^{2}}{2^{2} {(b^{4})}^{2}} \cdot \frac{5 b}{3 a}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Combine.

$\frac{3^{2} {(a^{2})}^{2} (5 b)}{2^{2} {(b^{4})}^{2} (3 a)}$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Factor $3$ out of $3^{2} {(a^{2})}^{2} (5 b)$ .

$\frac{3 (3 {(a^{2})}^{2} (5 b))}{2^{2} {(b^{4})}^{2} (3 a)}$

Step 3.2.2

Cancel the common factors.

Tap for more steps...

Step 3.2.2.1

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

$\frac{3 (3 {(a^{2})}^{2} (5 b))}{3 (2^{2} {(b^{4})}^{2} (a))}$

Step 3.2.2.2

Cancel the common factor.

$\frac{3 (3 {(a^{2})}^{2} (5 b))}{3 (2^{2} {(b^{4})}^{2} (a))}$

Step 3.2.2.3

Rewrite the expression.

$\frac{3 {(a^{2})}^{2} (5 b)}{2^{2} {(b^{4})}^{2} (a)}$

Step 3.3

Multiply $5$ by $3$ .

$\frac{15 {(a^{2})}^{2} b}{2^{2} {(b^{4})}^{2} a}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

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

$\frac{15 {(a^{2})}^{2} b}{4 {(b^{4})}^{2} a}$

Step 4.2

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

Tap for more steps...

Step 4.2.1

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

$\frac{15 {(a^{2})}^{2} b}{4 b^{4 \cdot 2} a}$

Step 4.2.2

Multiply $4$ by $2$ .

$\frac{15 {(a^{2})}^{2} b}{4 b^{8} a}$

Step 5

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 5.1

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

Tap for more steps...

Step 5.1.1

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

$\frac{15 a^{2 \cdot 2} b}{4 b^{8} a}$

Step 5.1.2

Multiply $2$ by $2$ .

$\frac{15 a^{4} b}{4 b^{8} a}$

Step 5.2

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

Tap for more steps...

Step 5.2.1

Factor $a$ out of $15 a^{4} b$ .

$\frac{a (15 a^{3} b)}{4 b^{8} a}$

Step 5.2.2

Cancel the common factors.

Tap for more steps...

Step 5.2.2.1

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

$\frac{a (15 a^{3} b)}{a (4 b^{8})}$

Step 5.2.2.2

Cancel the common factor.

$\frac{a (15 a^{3} b)}{a (4 b^{8})}$

Step 5.2.2.3

Rewrite the expression.

$\frac{15 a^{3} b}{4 b^{8}}$

Step 5.3

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

Tap for more steps...

Step 5.3.1

Factor $b$ out of $15 a^{3} b$ .

$\frac{b (15 a^{3})}{4 b^{8}}$

Step 5.3.2

Cancel the common factors.

Tap for more steps...

Step 5.3.2.1

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

$\frac{b (15 a^{3})}{b (4 b^{7})}$

Step 5.3.2.2

Cancel the common factor.

$\frac{b (15 a^{3})}{b (4 b^{7})}$

Step 5.3.2.3

Rewrite the expression.

$\frac{15 a^{3}}{4 b^{7}}$