Simplify ((-4a^2b)(-3a^7b))/(6a^7b^2)+16a^2

$\frac{(- 4 a^{2} b) (- 3 a^{7} b)}{6 a^{7} b^{2}} + 16 a^{2}$

Step 1

Simplify each term.

Multiply $a^{2}$ by $a^{7}$ by adding the exponents.

Move $a^{7}$ .

$\frac{- 4 (a^{7} a^{2}) b (- 3 b)}{6 a^{7} b^{2}} + 16 a^{2}$

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

$\frac{- 4 a^{7 + 2} b (- 3 b)}{6 a^{7} b^{2}} + 16 a^{2}$

Add $7$ and $2$ .

$\frac{- 4 a^{9} b (- 3 b)}{6 a^{7} b^{2}} + 16 a^{2}$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$\frac{- 4 a^{9} (b \cdot b) \cdot - 3}{6 a^{7} b^{2}} + 16 a^{2}$

Multiply $b$ by $b$ .

$\frac{- 4 a^{9} b^{2} \cdot - 3}{6 a^{7} b^{2}} + 16 a^{2}$

Cancel the common factor of $- 4$ and $6$ .

Factor $2$ out of $- 4 a^{9} b^{2} \cdot - 3$ .

$\frac{2 (- 2 a^{9} b^{2} \cdot - 3)}{6 a^{7} b^{2}} + 16 a^{2}$

Cancel the common factors.

Factor $2$ out of $6 a^{7} b^{2}$ .

$\frac{2 (- 2 a^{9} b^{2} \cdot - 3)}{2 (3 a^{7} b^{2})} + 16 a^{2}$

Cancel the common factor.

$\frac{2 (- 2 a^{9} b^{2} \cdot - 3)}{2 (3 a^{7} b^{2})} + 16 a^{2}$

Rewrite the expression.

$\frac{- 2 a^{9} b^{2} \cdot - 3}{3 a^{7} b^{2}} + 16 a^{2}$

Cancel the common factor of $a^{9}$ and $a^{7}$ .

Factor $a^{7}$ out of $- 2 a^{9} b^{2} \cdot - 3$ .

$\frac{a^{7} (- 2 a^{2} b^{2} \cdot - 3)}{3 a^{7} b^{2}} + 16 a^{2}$

Cancel the common factors.

Factor $a^{7}$ out of $3 a^{7} b^{2}$ .

$\frac{a^{7} (- 2 a^{2} b^{2} \cdot - 3)}{a^{7} (3 b^{2})} + 16 a^{2}$

Cancel the common factor.

$\frac{a^{7} (- 2 a^{2} b^{2} \cdot - 3)}{a^{7} (3 b^{2})} + 16 a^{2}$

Rewrite the expression.

$\frac{- 2 a^{2} b^{2} \cdot - 3}{3 b^{2}} + 16 a^{2}$

Cancel the common factor of $b^{2}$ .

Cancel the common factor.

$\frac{- 2 a^{2} b^{2} \cdot - 3}{3 b^{2}} + 16 a^{2}$

Rewrite the expression.

$\frac{- 2 a^{2} \cdot - 3}{3} + 16 a^{2}$

Cancel the common factor of $- 3$ and $3$ .

Factor $3$ out of $- 2 a^{2} \cdot - 3$ .

$\frac{3 (- 2 a^{2} \cdot - 1)}{3} + 16 a^{2}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (- 2 a^{2} \cdot - 1)}{3 (1)} + 16 a^{2}$

Cancel the common factor.

$\frac{3 (- 2 a^{2} \cdot - 1)}{3 \cdot 1} + 16 a^{2}$

Rewrite the expression.

$\frac{- 2 a^{2} \cdot - 1}{1} + 16 a^{2}$

Divide $- 2 a^{2} \cdot - 1$ by $1$ .

$- 2 a^{2} \cdot - 1 + 16 a^{2}$

Multiply $- 1$ by $- 2$ .

$2 a^{2} + 16 a^{2}$

Step 2

Add $2 a^{2}$ and $16 a^{2}$ .

$18 a^{2}$

Simplify ((-4a^2b)(-3a^7b))/(6a^7b^2)+16a^2

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