Algebra Examples

$\frac{{(- 8 x^{3} y^{2})}^{2} \cdot 2 x^{2} y^{6}}{32 x^{8} y^{3}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $2$ and $32$ .

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Step 1.1.1

Factor $2$ out of ${(- 8 x^{3} y^{2})}^{2} \cdot (2 x^{2} y^{6})$ .

$\frac{2 ({(- 8 x^{3} y^{2})}^{2} \cdot (x^{2} y^{6}))}{32 x^{8} y^{3}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $32 x^{8} y^{3}$ .

$\frac{2 ({(- 8 x^{3} y^{2})}^{2} \cdot (x^{2} y^{6}))}{2 (16 x^{8} y^{3})}$

Step 1.1.2.2

Cancel the common factor.

$\frac{2 ({(- 8 x^{3} y^{2})}^{2} \cdot (x^{2} y^{6}))}{2 (16 x^{8} y^{3})}$

Step 1.1.2.3

Rewrite the expression.

$\frac{{(- 8 x^{3} y^{2})}^{2} \cdot (x^{2} y^{6})}{16 x^{8} y^{3}}$

Step 1.2

Cancel the common factor of $x^{2}$ and $x^{8}$ .

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Step 1.2.1

Factor $x^{2}$ out of ${(- 8 x^{3} y^{2})}^{2} \cdot (x^{2} y^{6})$ .

$\frac{x^{2} ({(- 8 x^{3} y^{2})}^{2} \cdot (y^{6}))}{16 x^{8} y^{3}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $x^{2}$ out of $16 x^{8} y^{3}$ .

$\frac{x^{2} ({(- 8 x^{3} y^{2})}^{2} \cdot (y^{6}))}{x^{2} (16 x^{6} y^{3})}$

Step 1.2.2.2

Cancel the common factor.

$\frac{x^{2} ({(- 8 x^{3} y^{2})}^{2} \cdot (y^{6}))}{x^{2} (16 x^{6} y^{3})}$

Step 1.2.2.3

Rewrite the expression.

$\frac{{(- 8 x^{3} y^{2})}^{2} \cdot (y^{6})}{16 x^{6} y^{3}}$

Step 1.3

Cancel the common factor of $y^{6}$ and $y^{3}$ .

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Step 1.3.1

Factor $y^{3}$ out of ${(- 8 x^{3} y^{2})}^{2} \cdot (y^{6})$ .

$\frac{y^{3} ({(- 8 x^{3} y^{2})}^{2} \cdot (y^{3}))}{16 x^{6} y^{3}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $y^{3}$ out of $16 x^{6} y^{3}$ .

$\frac{y^{3} ({(- 8 x^{3} y^{2})}^{2} \cdot (y^{3}))}{y^{3} (16 x^{6})}$

Step 1.3.2.2

Cancel the common factor.

$\frac{y^{3} ({(- 8 x^{3} y^{2})}^{2} \cdot (y^{3}))}{y^{3} (16 x^{6})}$

Step 1.3.2.3

Rewrite the expression.

$\frac{{(- 8 x^{3} y^{2})}^{2} \cdot (y^{3})}{16 x^{6}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $- 8 x^{3} y^{2}$ .

$\frac{{(- 8 x^{3})}^{2} {(y^{2})}^{2} y^{3}}{16 x^{6}}$

Step 2.2

Apply the product rule to $- 8 x^{3}$ .

$\frac{{(- 8)}^{2} {(x^{3})}^{2} {(y^{2})}^{2} y^{3}}{16 x^{6}}$

Step 2.3

Raise $- 8$ to the power of $2$ .

$\frac{64 {(x^{3})}^{2} {(y^{2})}^{2} y^{3}}{16 x^{6}}$

Step 2.4

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

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Step 2.4.1

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

$\frac{64 x^{3 \cdot 2} {(y^{2})}^{2} y^{3}}{16 x^{6}}$

Step 2.4.2

Multiply $3$ by $2$ .

$\frac{64 x^{6} {(y^{2})}^{2} y^{3}}{16 x^{6}}$

Step 2.5

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

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Step 2.5.1

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

$\frac{64 x^{6} y^{2 \cdot 2} y^{3}}{16 x^{6}}$

Step 2.5.2

Multiply $2$ by $2$ .

$\frac{64 x^{6} y^{4} y^{3}}{16 x^{6}}$

Step 2.6

Multiply $y^{4}$ by $y^{3}$ by adding the exponents.

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Step 2.6.1

Move $y^{3}$ .

$\frac{64 x^{6} (y^{3} y^{4})}{16 x^{6}}$

Step 2.6.2

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

$\frac{64 x^{6} y^{3 + 4}}{16 x^{6}}$

Step 2.6.3

Add $3$ and $4$ .

$\frac{64 x^{6} y^{7}}{16 x^{6}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $64$ and $16$ .

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Step 3.1.1

Factor $16$ out of $64 x^{6} y^{7}$ .

$\frac{16 (4 x^{6} y^{7})}{16 x^{6}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $16$ out of $16 x^{6}$ .

$\frac{16 (4 x^{6} y^{7})}{16 (x^{6})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{16 (4 x^{6} y^{7})}{16 x^{6}}$

Step 3.1.2.3

Rewrite the expression.

$\frac{4 x^{6} y^{7}}{x^{6}}$

Step 3.2

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

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Step 3.2.1

Cancel the common factor.

$\frac{4 x^{6} y^{7}}{x^{6}}$

Step 3.2.2

Divide $4 y^{7}$ by $1$ .

$4 y^{7}$