Algebra Examples

$\frac{15 {(x^{- 2})}^{3}}{3 {(x^{- 4})}^{- 3}}$

Step 1

Move ${(x^{- 4})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{15 {(x^{- 2})}^{3} {(x^{- 4})}^{3}}{3}$

Step 2

Cancel the common factor of $15$ and $3$ .

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Step 2.1

Factor $3$ out of $15 {(x^{- 2})}^{3} {(x^{- 4})}^{3}$ .

$\frac{3 (5 {(x^{- 2})}^{3} {(x^{- 4})}^{3})}{3}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $3$ .

$\frac{3 (5 {(x^{- 2})}^{3} {(x^{- 4})}^{3})}{3 (1)}$

Step 2.2.2

Cancel the common factor.

$\frac{3 (5 {(x^{- 2})}^{3} {(x^{- 4})}^{3})}{3 \cdot 1}$

Step 2.2.3

Rewrite the expression.

$\frac{5 {(x^{- 2})}^{3} {(x^{- 4})}^{3}}{1}$

Step 2.2.4

Divide $5 {(x^{- 2})}^{3} {(x^{- 4})}^{3}$ by $1$ .

$5 {(x^{- 2})}^{3} {(x^{- 4})}^{3}$

Step 3

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

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Step 3.1

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

$5 x^{- 2 \cdot 3} {(x^{- 4})}^{3}$

Step 3.2

Multiply $- 2$ by $3$ .

$5 x^{- 6} {(x^{- 4})}^{3}$

Step 4

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

$5 \frac{1}{x^{6}} {(x^{- 4})}^{3}$

Step 5

Combine $5$ and $\frac{1}{x^{6}}$ .

$\frac{5}{x^{6}} {(x^{- 4})}^{3}$

Step 6

Multiply the exponents in ${(x^{- 4})}^{3}$ .

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Step 6.1

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

$\frac{5}{x^{6}} x^{- 4 \cdot 3}$

Step 6.2

Multiply $- 4$ by $3$ .

$\frac{5}{x^{6}} x^{- 12}$

Step 7

Cancel the common factor of $x^{- 12}$ .

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Step 7.1

Factor $x^{- 12}$ out of $x^{6}$ .

$\frac{5}{x^{- 12} x^{18}} x^{- 12}$

Step 7.2

Cancel the common factor.

$\frac{5}{x^{- 12} x^{18}} x^{- 12}$

Step 7.3

Rewrite the expression.

$\frac{5}{x^{18}}$