Algebra Examples

$(- \frac{4}{3} x y^{3}) \cdot (9 x^{8} y)$

Step 1

Multiply $x$ by $x^{8}$ by adding the exponents.

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Step 1.1

Move $x^{8}$ .

$- \frac{4}{3} \cdot (x^{8} x y^{3}) \cdot (9 y)$

Step 1.2

Multiply $x^{8}$ by $x$ .

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Step 1.2.1

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

$- \frac{4}{3} \cdot (x^{8} x^{1} y^{3}) \cdot (9 y)$

Step 1.2.2

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

$- \frac{4}{3} \cdot (x^{8 + 1} y^{3}) \cdot (9 y)$

Step 1.3

Add $8$ and $1$ .

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

Step 2

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

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Step 2.1

Move $y$ .

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

Step 2.2

Multiply $y$ by $y^{3}$ .

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Step 2.2.1

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

$- \frac{4}{3} \cdot (x^{9} (y^{1} y^{3})) \cdot 9$

Step 2.2.2

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

$- \frac{4}{3} \cdot (x^{9} y^{1 + 3}) \cdot 9$

Step 2.3

Add $1$ and $3$ .

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

Step 3

Multiply $- \frac{4}{3} (x^{9} y^{4})$ .

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Step 3.1

Combine $x^{9}$ and $\frac{4}{3}$ .

$- \frac{x^{9} \cdot 4}{3} y^{4} \cdot 9$

Step 3.2

Combine $y^{4}$ and $\frac{x^{9} \cdot 4}{3}$ .

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

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Move the leading negative in $- \frac{y^{4} x^{9} \cdot 4}{3}$ into the numerator.

$\frac{- y^{4} x^{9} \cdot 4}{3} \cdot 9$

Step 4.2

Factor $3$ out of $9$ .

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

Step 4.3

Cancel the common factor.

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

Step 4.4

Rewrite the expression.

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

Step 5

Multiply.

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Step 5.1

Multiply $4$ by $- 1$ .

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

Step 5.2

Multiply $3$ by $- 4$ .

$- 12 y^{4} x^{9}$