Algebra Examples

$(- 5 x^{6}) (2 x^{- 4} y) (- 6 x^{- 3} y^{4})$

Step 1

Multiply $x^{6}$ by $x^{- 4}$ by adding the exponents.

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Step 1.1

Move $x^{- 4}$ .

$- 5 (x^{- 4} x^{6}) (2 y) (- 6 x^{- 3} y^{4})$

Step 1.2

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

$- 5 x^{- 4 + 6} (2 y) (- 6 x^{- 3} y^{4})$

Step 1.3

Add $- 4$ and $6$ .

$- 5 x^{2} (2 y) (- 6 x^{- 3} y^{4})$

Step 2

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

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Step 2.1

Move $x^{- 3}$ .

$- 5 (x^{- 3} x^{2}) (2 y) (- 6 y^{4})$

Step 2.2

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

$- 5 x^{- 3 + 2} (2 y) (- 6 y^{4})$

Step 2.3

Add $- 3$ and $2$ .

$- 5 x^{- 1} (2 y) (- 6 y^{4})$

Step 3

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

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Step 3.1

Move $y^{4}$ .

$- 5 x^{- 1} (2 (y^{4} y)) \cdot - 6$

Step 3.2

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

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Step 3.2.1

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

$- 5 x^{- 1} (2 (y^{4} y^{1})) \cdot - 6$

Step 3.2.2

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

$- 5 x^{- 1} (2 y^{4 + 1}) \cdot - 6$

Step 3.3

Add $4$ and $1$ .

$- 5 x^{- 1} (2 y^{5}) \cdot - 6$

Step 4

Rewrite using the commutative property of multiplication.

$- 5 \cdot 2 x^{- 1} y^{5} \cdot - 6$

Step 5

Multiply $- 5$ by $2$ .

$- 10 x^{- 1} y^{5} \cdot - 6$

Step 6

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

$- 10 \frac{1}{x} y^{5} \cdot - 6$

Step 7

Combine $- 10$ and $\frac{1}{x}$ .

$\frac{- 10}{x} y^{5} \cdot - 6$

Step 8

Move the negative in front of the fraction.

$- \frac{10}{x} y^{5} \cdot - 6$

Step 9

Combine $y^{5}$ and $\frac{10}{x}$ .

$- \frac{y^{5} \cdot 10}{x} \cdot - 6$

Step 10

Move $10$ to the left of $y^{5}$ .

$- \frac{10 \cdot y^{5}}{x} \cdot - 6$

Step 11

Multiply $- \frac{10 y^{5}}{x} \cdot - 6$ .

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Step 11.1

Multiply $- 6$ by $- 1$ .

$6 \frac{10 y^{5}}{x}$

Step 11.2

Combine $6$ and $\frac{10 y^{5}}{x}$ .

$\frac{6 (10 y^{5})}{x}$

Step 11.3

Multiply $10$ by $6$ .

$\frac{60 y^{5}}{x}$