Pre-Algebra Examples

$\frac{{(12 x^{4} y^{- 16})}^{2} ({(3 x^{- 12} y^{5})}^{3})}{36 x^{- 14}}$

Step 1

Move $x^{- 14}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(12 x^{4} y^{- 16})}^{2} ({(3 x^{- 12} y^{5})}^{3}) x^{14}}{36}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $12 x^{4} y^{- 16}$ .

$\frac{{(12 x^{4})}^{2} {(y^{- 16})}^{2} {(3 x^{- 12} y^{5})}^{3} x^{14}}{36}$

Step 2.2

Apply the product rule to $3 x^{- 12} y^{5}$ .

$\frac{{(12 x^{4})}^{2} {(y^{- 16})}^{2} {(3 x^{- 12})}^{3} {(y^{5})}^{3} x^{14}}{36}$

Step 2.3

Apply the product rule to $12 x^{4}$ .

$\frac{12^{2} {(x^{4})}^{2} {(y^{- 16})}^{2} {(3 x^{- 12})}^{3} {(y^{5})}^{3} x^{14}}{36}$

Step 2.4

Raise $12$ to the power of $2$ .

$\frac{144 {(x^{4})}^{2} {(y^{- 16})}^{2} {(3 x^{- 12})}^{3} {(y^{5})}^{3} x^{14}}{36}$

Step 2.5

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

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Step 2.5.1

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

$\frac{144 x^{4 \cdot 2} {(y^{- 16})}^{2} {(3 x^{- 12})}^{3} {(y^{5})}^{3} x^{14}}{36}$

Step 2.5.2

Multiply $4$ by $2$ .

$\frac{144 x^{8} {(y^{- 16})}^{2} {(3 x^{- 12})}^{3} {(y^{5})}^{3} x^{14}}{36}$

Step 2.6

Multiply the exponents in ${(y^{- 16})}^{2}$ .

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Step 2.6.1

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

$\frac{144 x^{8} y^{- 16 \cdot 2} {(3 x^{- 12})}^{3} {(y^{5})}^{3} x^{14}}{36}$

Step 2.6.2

Multiply $- 16$ by $2$ .

$\frac{144 x^{8} y^{- 32} {(3 x^{- 12})}^{3} {(y^{5})}^{3} x^{14}}{36}$

Step 2.7

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{144 x^{8} \frac{1}{y^{32}} {(3 x^{- 12})}^{3} {(y^{5})}^{3} x^{14}}{36}$

Step 2.8

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{144 x^{8} \frac{1}{y^{32}} {(3 \frac{1}{x^{12}})}^{3} {(y^{5})}^{3} x^{14}}{36}$

Step 2.9

Combine $3$ and $\frac{1}{x^{12}}$ .

$\frac{144 x^{8} \frac{1}{y^{32}} {(\frac{3}{x^{12}})}^{3} {(y^{5})}^{3} x^{14}}{36}$

Step 2.10

Apply the product rule to $\frac{3}{x^{12}}$ .

$\frac{144 x^{8} \frac{1}{y^{32}} \frac{3^{3}}{{(x^{12})}^{3}} {(y^{5})}^{3} x^{14}}{36}$

Step 2.11

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

$\frac{144 x^{8} \frac{1}{y^{32}} \frac{27}{{(x^{12})}^{3}} {(y^{5})}^{3} x^{14}}{36}$

Step 2.12

Multiply the exponents in ${(x^{12})}^{3}$ .

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Step 2.12.1

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

$\frac{144 x^{8} \frac{1}{y^{32}} \frac{27}{x^{12 \cdot 3}} {(y^{5})}^{3} x^{14}}{36}$

Step 2.12.2

Multiply $12$ by $3$ .

$\frac{144 x^{8} \frac{1}{y^{32}} \frac{27}{x^{36}} {(y^{5})}^{3} x^{14}}{36}$

Step 2.13

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

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Step 2.13.1

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

$\frac{144 x^{8} \frac{1}{y^{32}} \frac{27}{x^{36}} y^{5 \cdot 3} x^{14}}{36}$

Step 2.13.2

Multiply $5$ by $3$ .

$\frac{144 x^{8} \frac{1}{y^{32}} \frac{27}{x^{36}} y^{15} x^{14}}{36}$

Step 2.14

Combine exponents.

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Step 2.14.1

Combine $144$ and $\frac{1}{y^{32}}$ .

$\frac{x^{8} \frac{144}{y^{32}} \frac{27}{x^{36}} y^{15} x^{14}}{36}$

Step 2.14.2

Combine $x^{8}$ and $\frac{144}{y^{32}}$ .

$\frac{\frac{x^{8} \cdot 144}{y^{32}} \cdot \frac{27}{x^{36}} y^{15} x^{14}}{36}$

Step 2.14.3

Multiply $\frac{x^{8} \cdot 144}{y^{32}}$ by $\frac{27}{x^{36}}$ .

$\frac{\frac{x^{8} \cdot 144 \cdot 27}{y^{32} x^{36}} y^{15} x^{14}}{36}$

Step 2.14.4

Multiply $27$ by $144$ .

$\frac{\frac{x^{8} \cdot 3888}{y^{32} x^{36}} y^{15} x^{14}}{36}$

Step 2.14.5

Combine $\frac{x^{8} \cdot 3888}{y^{32} x^{36}}$ and $y^{15}$ .

$\frac{\frac{x^{8} \cdot 3888 y^{15}}{y^{32} x^{36}} x^{14}}{36}$

Step 2.14.6

Combine $\frac{x^{8} \cdot 3888 y^{15}}{y^{32} x^{36}}$ and $x^{14}$ .

$\frac{\frac{x^{8} \cdot 3888 y^{15} x^{14}}{y^{32} x^{36}}}{36}$

Step 2.14.7

Multiply $x^{8}$ by $x^{14}$ by adding the exponents.

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Step 2.14.7.1

Move $x^{14}$ .

$\frac{\frac{x^{14} x^{8} \cdot 3888 y^{15}}{y^{32} x^{36}}}{36}$

Step 2.14.7.2

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

$\frac{\frac{x^{14 + 8} \cdot 3888 y^{15}}{y^{32} x^{36}}}{36}$

Step 2.14.7.3

Add $14$ and $8$ .

$\frac{\frac{x^{22} \cdot 3888 y^{15}}{y^{32} x^{36}}}{36}$

Step 2.15

Reduce the expression $\frac{x^{22} \cdot 3888 y^{15}}{y^{32} x^{36}}$ by cancelling the common factors.

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Step 2.15.1

Factor $x^{22}$ out of $x^{22} \cdot 3888 y^{15}$ .

$\frac{\frac{x^{22} (3888 y^{15})}{y^{32} x^{36}}}{36}$

Step 2.15.2

Factor $x^{22}$ out of $y^{32} x^{36}$ .

$\frac{\frac{x^{22} (3888 y^{15})}{x^{22} (y^{32} x^{14})}}{36}$

Step 2.15.3

Cancel the common factor.

$\frac{\frac{x^{22} (3888 y^{15})}{x^{22} (y^{32} x^{14})}}{36}$

Step 2.15.4

Rewrite the expression.

$\frac{\frac{3888 y^{15}}{y^{32} x^{14}}}{36}$

Step 2.16

Cancel the common factor of $y^{15}$ and $y^{32}$ .

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Step 2.16.1

Factor $y^{15}$ out of $3888 y^{15}$ .

$\frac{\frac{y^{15} \cdot 3888}{y^{32} x^{14}}}{36}$

Step 2.16.2

Cancel the common factors.

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Step 2.16.2.1

Factor $y^{15}$ out of $y^{32} x^{14}$ .

$\frac{\frac{y^{15} \cdot 3888}{y^{15} (y^{17} x^{14})}}{36}$

Step 2.16.2.2

Cancel the common factor.

$\frac{\frac{y^{15} \cdot 3888}{y^{15} (y^{17} x^{14})}}{36}$

Step 2.16.2.3

Rewrite the expression.

$\frac{\frac{3888}{y^{17} x^{14}}}{36}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{3888}{y^{17} x^{14}} \cdot \frac{1}{36}$

Step 4

Combine.

$\frac{3888 \cdot 1}{y^{17} x^{14} \cdot 36}$

Step 5

Cancel the common factor of $3888$ and $36$ .

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Step 5.1

Factor $36$ out of $3888 \cdot 1$ .

$\frac{36 (108 \cdot 1)}{y^{17} x^{14} \cdot 36}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $36$ out of $y^{17} x^{14} \cdot 36$ .

$\frac{36 (108 \cdot 1)}{36 \cdot (y^{17} x^{14})}$

Step 5.2.2

Cancel the common factor.

$\frac{36 (108 \cdot 1)}{36 \cdot (y^{17} x^{14})}$

Step 5.2.3

Rewrite the expression.

$\frac{108 \cdot 1}{y^{17} x^{14}}$

Step 6

Multiply $108$ by $1$ .

$\frac{108}{y^{17} x^{14}}$