Algebra Examples

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

Step 1

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

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Step 1.1

Move $y^{2}$ .

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

Step 1.2

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

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

Step 1.3

Add $2$ and $3$ .

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

Step 2

Multiply $y^{5}$ by $y^{4}$ by adding the exponents.

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Step 2.1

Move $y^{4}$ .

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

Step 2.2

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

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

Step 2.3

Add $4$ and $5$ .

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

Step 3

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

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Step 3.1

Move $x$ .

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

Step 3.2

Multiply $x$ by $x^{2}$ .

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Step 3.2.1

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

$8 y^{9} (- 3 (x^{1} x^{2})) \frac{3}{8}$

Step 3.2.2

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

$8 y^{9} (- 3 x^{1 + 2}) \frac{3}{8}$

Step 3.3

Add $1$ and $2$ .

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

Step 4

Simplify the expression.

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Step 4.1

Rewrite using the commutative property of multiplication.

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

Step 4.2

Multiply $8$ by $- 3$ .

$- 24 y^{9} x^{3} \frac{3}{8}$

Step 5

Cancel the common factor of $8$ .

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Step 5.1

Factor $8$ out of $- 24 y^{9} x^{3}$ .

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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

Step 6

Multiply $3$ by $- 3$ .

$- 9 y^{9} x^{3}$