Algebra Examples

$\frac{{(2 x^{3} y^{2})}^{3}}{{(3 x y)}^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $2 x^{3} y^{2}$ .

$\frac{{(2 x^{3})}^{3} {(y^{2})}^{3}}{{(3 x y)}^{2}}$

Step 1.2

Apply the product rule to $2 x^{3}$ .

$\frac{2^{3} {(x^{3})}^{3} {(y^{2})}^{3}}{{(3 x y)}^{2}}$

Step 1.3

Raise $2$ to the power of $3$ .

$\frac{8 {(x^{3})}^{3} {(y^{2})}^{3}}{{(3 x y)}^{2}}$

Step 1.4

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

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Step 1.4.1

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

$\frac{8 x^{3 \cdot 3} {(y^{2})}^{3}}{{(3 x y)}^{2}}$

Step 1.4.2

Multiply $3$ by $3$ .

$\frac{8 x^{9} {(y^{2})}^{3}}{{(3 x y)}^{2}}$

Step 1.5

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

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Step 1.5.1

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

$\frac{8 x^{9} y^{2 \cdot 3}}{{(3 x y)}^{2}}$

Step 1.5.2

Multiply $2$ by $3$ .

$\frac{8 x^{9} y^{6}}{{(3 x y)}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $3 x y$ .

$\frac{8 x^{9} y^{6}}{{(3 x)}^{2} y^{2}}$

Step 2.2

Apply the product rule to $3 x$ .

$\frac{8 x^{9} y^{6}}{3^{2} x^{2} y^{2}}$

Step 2.3

Raise $3$ to the power of $2$ .

$\frac{8 x^{9} y^{6}}{9 x^{2} y^{2}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $x^{9}$ and $x^{2}$ .

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Step 3.1.1

Factor $x^{2}$ out of $8 x^{9} y^{6}$ .

$\frac{x^{2} (8 x^{7} y^{6})}{9 x^{2} y^{2}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

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

$\frac{x^{2} (8 x^{7} y^{6})}{x^{2} (9 y^{2})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{x^{2} (8 x^{7} y^{6})}{x^{2} (9 y^{2})}$

Step 3.1.2.3

Rewrite the expression.

$\frac{8 x^{7} y^{6}}{9 y^{2}}$

Step 3.2

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

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Step 3.2.1

Factor $y^{2}$ out of $8 x^{7} y^{6}$ .

$\frac{y^{2} (8 x^{7} y^{4})}{9 y^{2}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $y^{2}$ out of $9 y^{2}$ .

$\frac{y^{2} (8 x^{7} y^{4})}{y^{2} \cdot 9}$

Step 3.2.2.2

Cancel the common factor.

$\frac{y^{2} (8 x^{7} y^{4})}{y^{2} \cdot 9}$

Step 3.2.2.3

Rewrite the expression.

$\frac{8 x^{7} y^{4}}{9}$