Algebra Examples

${(x^{3} y^{6})}^{- 2} + {(x^{2} y^{4})}^{- 3}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{1}{{(x^{3} y^{6})}^{2}} + {(x^{2} y^{4})}^{- 3}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

Apply the product rule to $x^{3} y^{6}$ .

$\frac{1}{{(x^{3})}^{2} {(y^{6})}^{2}} + {(x^{2} y^{4})}^{- 3}$

Step 1.2.2

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

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Step 1.2.2.1

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

$\frac{1}{x^{3 \cdot 2} {(y^{6})}^{2}} + {(x^{2} y^{4})}^{- 3}$

Step 1.2.2.2

Multiply $3$ by $2$ .

$\frac{1}{x^{6} {(y^{6})}^{2}} + {(x^{2} y^{4})}^{- 3}$

Step 1.2.3

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

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Step 1.2.3.1

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

$\frac{1}{x^{6} y^{6 \cdot 2}} + {(x^{2} y^{4})}^{- 3}$

Step 1.2.3.2

Multiply $6$ by $2$ .

$\frac{1}{x^{6} y^{12}} + {(x^{2} y^{4})}^{- 3}$

Step 1.3

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

$\frac{1}{x^{6} y^{12}} + \frac{1}{{(x^{2} y^{4})}^{3}}$

Step 1.4

Simplify the denominator.

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Step 1.4.1

Apply the product rule to $x^{2} y^{4}$ .

$\frac{1}{x^{6} y^{12}} + \frac{1}{{(x^{2})}^{3} {(y^{4})}^{3}}$

Step 1.4.2

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

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Step 1.4.2.1

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

$\frac{1}{x^{6} y^{12}} + \frac{1}{x^{2 \cdot 3} {(y^{4})}^{3}}$

Step 1.4.2.2

Multiply $2$ by $3$ .

$\frac{1}{x^{6} y^{12}} + \frac{1}{x^{6} {(y^{4})}^{3}}$

Step 1.4.3

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

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Step 1.4.3.1

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

$\frac{1}{x^{6} y^{12}} + \frac{1}{x^{6} y^{4 \cdot 3}}$

Step 1.4.3.2

Multiply $4$ by $3$ .

$\frac{1}{x^{6} y^{12}} + \frac{1}{x^{6} y^{12}}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{1 + 1}{y^{12} x^{6}}$

Step 2.2

Add $1$ and $1$ .

$\frac{2}{y^{12} x^{6}}$