Simplify -6a^2b^-4c*4ab^2

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

Step 1

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

Move $a$ .

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

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

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

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

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

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

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.

Move $b^{2}$ .

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

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

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

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

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

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

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

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

Step 5

Simplify the expression.

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

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

Move the negative in front of the fraction.

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

Step 6

Multiply $6$ by $a^{3}$ .

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

Step 7

Combine fractions.

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

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

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

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

Step 8

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

Multiply $4$ by $- 1$ .

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

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

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

Multiply $6$ by $- 4$ .

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

Step 9

Move the negative in front of the fraction.

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

Simplify -6a^2b^-4c*4ab^2

Related Questions

Support LCMGCF.com by disabling your adblocker.