Basic Math Examples

${(\frac{9 a^{7} b^{8} c^{3}}{3 a^{4} b^{2} c})}^{2}$

Step 1

Cancel the common factor of $9$ and $3$ .

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Step 1.1

Factor $3$ out of $9 a^{7} b^{8} c^{3}$ .

${(\frac{3 (3 a^{7} b^{8} c^{3})}{3 a^{4} b^{2} c})}^{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

${(\frac{3 (3 a^{7} b^{8} c^{3})}{3 (a^{4} b^{2} c)})}^{2}$

Step 1.2.2

Cancel the common factor.

${(\frac{3 (3 a^{7} b^{8} c^{3})}{3 (a^{4} b^{2} c)})}^{2}$

Step 1.2.3

Rewrite the expression.

${(\frac{3 a^{7} b^{8} c^{3}}{a^{4} b^{2} c})}^{2}$

Step 2

Cancel the common factor of $a^{7}$ and $a^{4}$ .

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Step 2.1

Factor $a^{4}$ out of $3 a^{7} b^{8} c^{3}$ .

${(\frac{a^{4} (3 a^{3} b^{8} c^{3})}{a^{4} b^{2} c})}^{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

${(\frac{a^{4} (3 a^{3} b^{8} c^{3})}{a^{4} (b^{2} c)})}^{2}$

Step 2.2.2

Cancel the common factor.

${(\frac{a^{4} (3 a^{3} b^{8} c^{3})}{a^{4} (b^{2} c)})}^{2}$

Step 2.2.3

Rewrite the expression.

${(\frac{3 a^{3} b^{8} c^{3}}{b^{2} c})}^{2}$

Step 3

Cancel the common factor of $b^{8}$ and $b^{2}$ .

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Step 3.1

Factor $b^{2}$ out of $3 a^{3} b^{8} c^{3}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

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

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

Step 4.2.3

Cancel the common factor.

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

Step 4.2.4

Rewrite the expression.

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

Step 4.2.5

Divide $3 a^{3} b^{6} c^{2}$ by $1$ .

${(3 a^{3} b^{6} c^{2})}^{2}$

Step 5

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

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Step 5.1

Apply the product rule to $3 a^{3} b^{6} c^{2}$ .

${(3 a^{3} b^{6})}^{2} {(c^{2})}^{2}$

Step 5.2

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

${(3 a^{3})}^{2} {(b^{6})}^{2} {(c^{2})}^{2}$

Step 5.3

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

$3^{2} {(a^{3})}^{2} {(b^{6})}^{2} {(c^{2})}^{2}$

Step 6

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

$9 {(a^{3})}^{2} {(b^{6})}^{2} {(c^{2})}^{2}$

Step 7

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

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Step 7.1

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

$9 a^{3 \cdot 2} {(b^{6})}^{2} {(c^{2})}^{2}$

Step 7.2

Multiply $3$ by $2$ .

$9 a^{6} {(b^{6})}^{2} {(c^{2})}^{2}$

Step 8

Multiply the exponents in ${(b^{6})}^{2}$ .

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Step 8.1

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

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

Step 8.2

Multiply $6$ by $2$ .

$9 a^{6} b^{12} {(c^{2})}^{2}$

Step 9

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

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Step 9.1

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

$9 a^{6} b^{12} c^{2 \cdot 2}$

Step 9.2

Multiply $2$ by $2$ .

$9 a^{6} b^{12} c^{4}$