Basic Math Examples

${(\frac{a^{7} b^{9} c^{4}}{a^{2} b^{3} c})}^{3}$

Step 1

Cancel the common factor of $a^{7}$ and $a^{2}$ .

Tap for more steps...

Step 1.1

Factor $a^{2}$ out of $a^{7} b^{9} c^{4}$ .

${(\frac{a^{2} (a^{5} b^{9} c^{4})}{a^{2} b^{3} c})}^{3}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

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

${(\frac{a^{2} (a^{5} b^{9} c^{4})}{a^{2} (b^{3} c)})}^{3}$

Step 1.2.2

Cancel the common factor.

${(\frac{a^{2} (a^{5} b^{9} c^{4})}{a^{2} (b^{3} c)})}^{3}$

Step 1.2.3

Rewrite the expression.

${(\frac{a^{5} b^{9} c^{4}}{b^{3} c})}^{3}$

Step 2

Cancel the common factor of $b^{9}$ and $b^{3}$ .

Tap for more steps...

Step 2.1

Factor $b^{3}$ out of $a^{5} b^{9} c^{4}$ .

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

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $b^{3}$ out of $b^{3} c$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

Tap for more steps...

Step 3.1

Factor $c$ out of $a^{5} b^{6} c^{4}$ .

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

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Raise $c$ to the power of $1$ .

${(\frac{c (a^{5} b^{6} c^{3})}{c^{1}})}^{3}$

Step 3.2.2

Factor $c$ out of $c^{1}$ .

${(\frac{c (a^{5} b^{6} c^{3})}{c \cdot 1})}^{3}$

Step 3.2.3

Cancel the common factor.

${(\frac{c (a^{5} b^{6} c^{3})}{c \cdot 1})}^{3}$

Step 3.2.4

Rewrite the expression.

${(\frac{a^{5} b^{6} c^{3}}{1})}^{3}$

Step 3.2.5

Divide $a^{5} b^{6} c^{3}$ by $1$ .

${(a^{5} b^{6} c^{3})}^{3}$

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 $a^{5} b^{6} c^{3}$ .

${(a^{5} b^{6})}^{3} {(c^{3})}^{3}$

Step 4.2

Apply the product rule to $a^{5} b^{6}$ .

${(a^{5})}^{3} {(b^{6})}^{3} {(c^{3})}^{3}$

Step 5

Multiply the exponents in ${(a^{5})}^{3}$ .

Tap for more steps...

Step 5.1

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

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

Step 5.2

Multiply $5$ by $3$ .

$a^{15} {(b^{6})}^{3} {(c^{3})}^{3}$

Step 6

Multiply the exponents in ${(b^{6})}^{3}$ .

Tap for more steps...

Step 6.1

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

$a^{15} b^{6 \cdot 3} {(c^{3})}^{3}$

Step 6.2

Multiply $6$ by $3$ .

$a^{15} b^{18} {(c^{3})}^{3}$

Step 7

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

Tap for more steps...

Step 7.1

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

$a^{15} b^{18} c^{3 \cdot 3}$

Step 7.2

Multiply $3$ by $3$ .

$a^{15} b^{18} c^{9}$