Algebra Examples

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

Step 1

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 1.1

Move $x^{2}$ .

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

Step 1.2

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

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

Step 1.3

Add $2$ and $2$ .

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

Step 2

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

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Step 2.1

Move $y^{4}$ .

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

Step 2.2

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

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

Step 2.3

Add $4$ and $4$ .

$\frac{2 x^{4} y^{8} \cdot 4 \cdot (3 x)}{3 x^{- 3} y^{2}}$

Step 3

Multiply $x^{4}$ by $x$ by adding the exponents.

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Step 3.1

Move $x$ .

$\frac{2 (x \cdot x^{4}) y^{8} \cdot 4 \cdot 3}{3 x^{- 3} y^{2}}$

Step 3.2

Multiply $x$ by $x^{4}$ .

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Step 3.2.1

Raise $x$ to the power of $1$ .

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

Step 3.2.2

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

$\frac{2 x^{1 + 4} y^{8} \cdot 4 \cdot 3}{3 x^{- 3} y^{2}}$

Step 3.3

Add $1$ and $4$ .

$\frac{2 x^{5} y^{8} \cdot 4 \cdot 3}{3 x^{- 3} y^{2}}$

Step 4

Move $x^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{2 x^{5} y^{8} \cdot 4 \cdot 3 x^{3}}{3 y^{2}}$

Step 5

Multiply $x^{5}$ by $x^{3}$ by adding the exponents.

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Step 5.1

Move $x^{3}$ .

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

Step 5.2

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

$\frac{2 x^{3 + 5} y^{8} \cdot 4 \cdot 3}{3 y^{2}}$

Step 5.3

Add $3$ and $5$ .

$\frac{2 x^{8} y^{8} \cdot 4 \cdot 3}{3 y^{2}}$

Step 6

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

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Step 6.1

Factor $y^{2}$ out of $2 x^{8} y^{8} \cdot 4 \cdot 3$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $y^{2}$ out of $3 y^{2}$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

$\frac{2 x^{8} y^{6} \cdot 4 \cdot 3}{3}$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Cancel the common factor.

$\frac{2 x^{8} y^{6} \cdot 4 \cdot 3}{3}$

Step 7.2

Divide $2 x^{8} y^{6} \cdot 4$ by $1$ .

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

Step 8

Multiply $4$ by $2$ .

$8 x^{8} y^{6}$