Basic Math Examples

${(\frac{50 a^{13} b^{- 8} c^{6}}{10 a^{9} b^{- 2} c^{4}})}^{- 2}$

Step 1

Move $b^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{50 a^{13} c^{6}}{10 a^{9} b^{- 2} c^{4} b^{8}})}^{- 2}$

Step 2

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

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Step 2.1

Move $b^{8}$ .

${(\frac{50 a^{13} c^{6}}{10 a^{9} (b^{8} b^{- 2}) c^{4}})}^{- 2}$

Step 2.2

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

${(\frac{50 a^{13} c^{6}}{10 a^{9} b^{8 - 2} c^{4}})}^{- 2}$

Step 2.3

Subtract $2$ from $8$ .

${(\frac{50 a^{13} c^{6}}{10 a^{9} b^{6} c^{4}})}^{- 2}$

Step 3

Cancel the common factor of $50$ and $10$ .

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Step 3.1

Factor $10$ out of $50 a^{13} c^{6}$ .

${(\frac{10 (5 a^{13} c^{6})}{10 a^{9} b^{6} c^{4}})}^{- 2}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $10$ out of $10 a^{9} b^{6} c^{4}$ .

${(\frac{10 (5 a^{13} c^{6})}{10 (a^{9} b^{6} c^{4})})}^{- 2}$

Step 3.2.2

Cancel the common factor.

${(\frac{10 (5 a^{13} c^{6})}{10 (a^{9} b^{6} c^{4})})}^{- 2}$

Step 3.2.3

Rewrite the expression.

${(\frac{5 a^{13} c^{6}}{a^{9} b^{6} c^{4}})}^{- 2}$

Step 4

Cancel the common factor of $a^{13}$ and $a^{9}$ .

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Step 4.1

Factor $a^{9}$ out of $5 a^{13} c^{6}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a^{9}$ out of $a^{9} b^{6} c^{4}$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 7

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

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Step 7.1

Apply the product rule to $\frac{b^{6}}{5 a^{4} c^{2}}$ .

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

Step 7.2

Apply the product rule to $5 a^{4} c^{2}$ .

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

Step 7.3

Apply the product rule to $5 a^{4}$ .

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

Step 8

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

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Step 8.1

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

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

Step 8.2

Multiply $6$ by $2$ .

$\frac{b^{12}}{5^{2} {(a^{4})}^{2} {(c^{2})}^{2}}$

Step 9

Simplify the denominator.

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Step 9.1

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

$\frac{b^{12}}{25 {(a^{4})}^{2} {(c^{2})}^{2}}$

Step 9.2

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

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Step 9.2.1

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

$\frac{b^{12}}{25 a^{4 \cdot 2} {(c^{2})}^{2}}$

Step 9.2.2

Multiply $4$ by $2$ .

$\frac{b^{12}}{25 a^{8} {(c^{2})}^{2}}$

Step 9.3

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

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Step 9.3.1

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

$\frac{b^{12}}{25 a^{8} c^{2 \cdot 2}}$

Step 9.3.2

Multiply $2$ by $2$ .

$\frac{b^{12}}{25 a^{8} c^{4}}$