Algebra Examples

$- 6 a^{2} b^{- 4} c \cdot 4 a b^{2}$

Step 1

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

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Step 1.1

Move $a$ .

$- 6 (a \cdot a^{2}) b^{- 4} c \cdot (4 b^{2})$

Step 1.2

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

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Step 1.2.1

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

$- 6 (a^{1} a^{2}) b^{- 4} c \cdot (4 b^{2})$

Step 1.2.2

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

$- 6 a^{1 + 2} b^{- 4} c \cdot (4 b^{2})$

Step 1.3

Add $1$ and $2$ .

$- 6 a^{3} b^{- 4} c \cdot (4 b^{2})$

Step 2

Multiply $b^{- 4}$ by $b^{2}$ by adding the exponents.

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Step 2.1

Move $b^{2}$ .

$- 6 a^{3} (b^{2} b^{- 4}) c \cdot 4$

Step 2.2

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

$- 6 a^{3} b^{2 - 4} c \cdot 4$

Step 2.3

Subtract $4$ from $2$ .

$- 6 a^{3} b^{- 2} c \cdot 4$

Step 3

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

$- 6 a^{3} \frac{1}{b^{2}} c \cdot 4$

Step 4

Multiply $- 6 a^{3} \frac{1}{b^{2}}$ .

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Step 4.1

Combine $- 6$ and $\frac{1}{b^{2}}$ .

$a^{3} \frac{- 6}{b^{2}} c \cdot 4$

Step 4.2

Combine $a^{3}$ and $\frac{- 6}{b^{2}}$ .

$\frac{a^{3} \cdot - 6}{b^{2}} c \cdot 4$

Step 5

Simplify the expression.

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Step 5.1

Move $- 6$ to the left of $a^{3}$ .

$\frac{- 6 \cdot a^{3}}{b^{2}} c \cdot 4$

Step 5.2

Move the negative in front of the fraction.

$- \frac{6 \cdot a^{3}}{b^{2}} c \cdot 4$

Step 6

Combine $c$ and $\frac{6 a^{3}}{b^{2}}$ .

$- \frac{c (6 a^{3})}{b^{2}} \cdot 4$

Step 7

Move $6$ to the left of $c$ .

$- \frac{6 \cdot c a^{3}}{b^{2}} \cdot 4$

Step 8

Multiply $- \frac{6 c a^{3}}{b^{2}} \cdot 4$ .

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Step 8.1

Multiply $4$ by $- 1$ .

$- 4 \frac{6 c a^{3}}{b^{2}}$

Step 8.2

Combine $- 4$ and $\frac{6 c a^{3}}{b^{2}}$ .

$\frac{- 4 (6 c a^{3})}{b^{2}}$

Step 8.3

Multiply $6$ by $- 4$ .

$\frac{- 24 (c a^{3})}{b^{2}}$

Step 9

Move the negative in front of the fraction.

$- \frac{24 c a^{3}}{b^{2}}$