Algebra Examples

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

Step 1

Apply the product rule to $x^{3} y^{4}$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Multiply $3$ by $3$ .

$x^{9} {(y^{4})}^{3} \cdot {(x y^{3})}^{- 2}$

Step 3

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

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Step 3.1

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

$x^{9} y^{4 \cdot 3} \cdot {(x y^{3})}^{- 2}$

Step 3.2

Multiply $4$ by $3$ .

$x^{9} y^{12} \cdot {(x y^{3})}^{- 2}$

Step 4

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

$x^{9} y^{12} \cdot \frac{1}{{(x y^{3})}^{2}}$

Step 5

Simplify the denominator.

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Step 5.1

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

$x^{9} y^{12} \cdot \frac{1}{x^{2} {(y^{3})}^{2}}$

Step 5.2

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

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Step 5.2.1

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

$x^{9} y^{12} \cdot \frac{1}{x^{2} y^{3 \cdot 2}}$

Step 5.2.2

Multiply $3$ by $2$ .

$x^{9} y^{12} \cdot \frac{1}{x^{2} y^{6}}$

Step 6

Cancel the common factor of $x^{2} y^{6}$ .

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Step 6.1

Factor $x^{2} y^{6}$ out of $x^{9} y^{12}$ .

$x^{2} y^{6} (x^{7} y^{6}) \cdot \frac{1}{x^{2} y^{6}}$

Step 6.2

Cancel the common factor.

$x^{2} y^{6} (x^{7} y^{6}) \cdot \frac{1}{x^{2} y^{6}}$

Step 6.3

Rewrite the expression.

$x^{7} y^{6}$