Algebra Examples

$\frac{12 x^{5} y^{8}}{3 y^{3}} \cdot \frac{2 {(x^{6})}^{2}}{y^{- 3}}$

Step 1

Combine.

$\frac{12 x^{5} y^{8} (2 {(x^{6})}^{2})}{3 y^{3} y^{- 3}}$

Step 2

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

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Step 2.1

Move $y^{- 3}$ .

$\frac{12 x^{5} y^{8} (2 {(x^{6})}^{2})}{3 (y^{- 3} y^{3})}$

Step 2.2

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

$\frac{12 x^{5} y^{8} (2 {(x^{6})}^{2})}{3 y^{- 3 + 3}}$

Step 2.3

Add $- 3$ and $3$ .

$\frac{12 x^{5} y^{8} (2 {(x^{6})}^{2})}{3 y^{0}}$

Step 3

Simplify $3 y^{0}$ .

$\frac{12 x^{5} y^{8} (2 {(x^{6})}^{2})}{3}$

Step 4

Cancel the common factor of $12$ and $3$ .

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Step 4.1

Factor $3$ out of $12 x^{5} y^{8} (2 {(x^{6})}^{2})$ .

$\frac{3 (4 x^{5} y^{8} (2 {(x^{6})}^{2}))}{3}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $3$ .

$\frac{3 (4 x^{5} y^{8} (2 {(x^{6})}^{2}))}{3 (1)}$

Step 4.2.2

Cancel the common factor.

$\frac{3 (4 x^{5} y^{8} (2 {(x^{6})}^{2}))}{3 \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{4 x^{5} y^{8} (2 {(x^{6})}^{2})}{1}$

Step 4.2.4

Divide $4 x^{5} y^{8} (2 {(x^{6})}^{2})$ by $1$ .

$4 x^{5} y^{8} (2 {(x^{6})}^{2})$

Step 5

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

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Step 5.1

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

$4 x^{5} y^{8} (2 x^{6 \cdot 2})$

Step 5.2

Multiply $6$ by $2$ .

$4 x^{5} y^{8} (2 x^{12})$

Step 6

Multiply $x^{5}$ by $x^{12}$ by adding the exponents.

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Step 6.1

Move $x^{12}$ .

$4 (x^{12} x^{5}) y^{8} \cdot 2$

Step 6.2

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

$4 x^{12 + 5} y^{8} \cdot 2$

Step 6.3

Add $12$ and $5$ .

$4 x^{17} y^{8} \cdot 2$

Step 7

Multiply $2$ by $4$ .

$8 x^{17} y^{8}$