Algebra Examples

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

Step 1

Multiply $x^{3}$ by $x^{- 8}$ by adding the exponents.

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Step 1.1

Move $x^{- 8}$ .

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

Step 1.2

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

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

Step 1.3

Add $- 8$ and $3$ .

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

Step 2

Multiply $y^{- 2}$ by $y^{5}$ by adding the exponents.

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Step 2.1

Move $y^{5}$ .

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

Step 2.2

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

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

Step 2.3

Subtract $2$ from $5$ .

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Multiply $- 4$ by $2$ .

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

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- 8 \frac{1}{x^{5}} y^{3} \cdot 5$

Step 6

Combine $- 8$ and $\frac{1}{x^{5}}$ .

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

Step 7

Move the negative in front of the fraction.

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

Step 8

Combine $y^{3}$ and $\frac{8}{x^{5}}$ .

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

Step 9

Move $8$ to the left of $y^{3}$ .

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

Step 10

Multiply $- \frac{8 y^{3}}{x^{5}} \cdot 5$ .

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Step 10.1

Multiply $5$ by $- 1$ .

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

Step 10.2

Combine $- 5$ and $\frac{8 y^{3}}{x^{5}}$ .

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

Step 10.3

Multiply $8$ by $- 5$ .

$\frac{- 40 y^{3}}{x^{5}}$

Step 11

Move the negative in front of the fraction.

$- \frac{40 y^{3}}{x^{5}}$