Algebra Examples

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

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 $\frac{a^{3} b^{2}}{3 c^{4}}$ .

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

Step 1.2

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

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

Step 1.3

Apply the product rule to $3 c^{4}$ .

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

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

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

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

Step 2.1.2

Multiply $3$ by $2$ .

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

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

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

Step 2.2.2

Multiply $2$ by $2$ .

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

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

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

$\frac{a^{6} b^{4}}{9 {(c^{4})}^{2}} {(\frac{5 a b^{2}}{c})}^{2}$

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

$\frac{a^{6} b^{4}}{9 c^{4 \cdot 2}} {(\frac{5 a b^{2}}{c})}^{2}$

Step 3.2.2

Multiply $4$ by $2$ .

$\frac{a^{6} b^{4}}{9 c^{8}} {(\frac{5 a b^{2}}{c})}^{2}$

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 $\frac{5 a b^{2}}{c}$ .

$\frac{a^{6} b^{4}}{9 c^{8}} \cdot \frac{{(5 a b^{2})}^{2}}{c^{2}}$

Step 4.2

Apply the product rule to $5 a b^{2}$ .

$\frac{a^{6} b^{4}}{9 c^{8}} \cdot \frac{{(5 a)}^{2} {(b^{2})}^{2}}{c^{2}}$

Step 4.3

Apply the product rule to $5 a$ .

$\frac{a^{6} b^{4}}{9 c^{8}} \cdot \frac{5^{2} a^{2} {(b^{2})}^{2}}{c^{2}}$

Step 5

Combine.

$\frac{a^{6} b^{4} (5^{2} a^{2} {(b^{2})}^{2})}{9 c^{8} c^{2}}$

Step 6

Multiply $a^{6}$ by $a^{2}$ by adding the exponents.

Tap for more steps...

Step 6.1

Move $a^{2}$ .

$\frac{a^{2} a^{6} b^{4} (5^{2} {(b^{2})}^{2})}{9 c^{8} c^{2}}$

Step 6.2

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

$\frac{a^{2 + 6} b^{4} (5^{2} {(b^{2})}^{2})}{9 c^{8} c^{2}}$

Step 6.3

Add $2$ and $6$ .

$\frac{a^{8} b^{4} (5^{2} {(b^{2})}^{2})}{9 c^{8} c^{2}}$

Step 7

Multiply $c^{8}$ by $c^{2}$ by adding the exponents.

Tap for more steps...

Step 7.1

Move $c^{2}$ .

$\frac{a^{8} b^{4} (5^{2} {(b^{2})}^{2})}{9 (c^{2} c^{8})}$

Step 7.2

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

$\frac{a^{8} b^{4} (5^{2} {(b^{2})}^{2})}{9 c^{2 + 8}}$

Step 7.3

Add $2$ and $8$ .

$\frac{a^{8} b^{4} (5^{2} {(b^{2})}^{2})}{9 c^{10}}$

Step 8

Simplify the numerator.

Tap for more steps...

Step 8.1

Rewrite.

$\frac{a^{6} b^{4} (5^{2} a^{2} {(b^{2})}^{2})}{9 c^{10}}$

Step 8.2

Remove unnecessary parentheses.

$\frac{a^{8} b^{4} \cdot 5^{2} {(b^{2})}^{2}}{9 c^{10}}$

Step 8.3

Raise $5$ to the power of $2$ .

$\frac{a^{8} b^{4} \cdot 25 {(b^{2})}^{2}}{9 c^{10}}$

Step 8.4

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

Tap for more steps...

Step 8.4.1

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

$\frac{a^{8} b^{4} \cdot 25 b^{2 \cdot 2}}{9 c^{10}}$

Step 8.4.2

Multiply $2$ by $2$ .

$\frac{a^{8} b^{4} \cdot 25 b^{4}}{9 c^{10}}$

Step 8.5

Multiply $b^{4}$ by $b^{4}$ by adding the exponents.

Tap for more steps...

Step 8.5.1

Move $b^{4}$ .

$\frac{a^{8} (b^{4} b^{4}) \cdot 25}{9 c^{10}}$

Step 8.5.2

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

$\frac{a^{8} b^{4 + 4} \cdot 25}{9 c^{10}}$

Step 8.5.3

Add $4$ and $4$ .

$\frac{a^{8} b^{8} \cdot 25}{9 c^{10}}$

Step 9

Move $25$ to the left of $a^{8} b^{8}$ .

$\frac{25 a^{8} b^{8}}{9 c^{10}}$