Simplify -3f^2g^-3(2(fg))(7f^3g^-2)

$- 3 f^{2} g^{- 3} (2 (f g)) (7 f^{3} g^{- 2})$

Step 1

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

Move $f$ .

$- 3 (f \cdot f^{2}) g^{- 3} (2 (g)) (7 f^{3} g^{- 2})$

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

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

$- 3 (f^{1} f^{2}) g^{- 3} (2 (g)) (7 f^{3} g^{- 2})$

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

$- 3 f^{1 + 2} g^{- 3} (2 (g)) (7 f^{3} g^{- 2})$

Add $1$ and $2$ .

$- 3 f^{3} g^{- 3} (2 (g)) (7 f^{3} g^{- 2})$

Step 2

Multiply $f^{3}$ by $f^{3}$ by adding the exponents.

Move $f^{3}$ .

$- 3 (f^{3} f^{3}) g^{- 3} (2 (g)) (7 g^{- 2})$

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

$- 3 f^{3 + 3} g^{- 3} (2 (g)) (7 g^{- 2})$

Add $3$ and $3$ .

$- 3 f^{6} g^{- 3} (2 (g)) (7 g^{- 2})$

Step 3

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

Move $g$ .

$- 3 f^{6} (g \cdot g^{- 3}) \cdot 2 (7 g^{- 2})$

Multiply $g$ by $g^{- 3}$ .

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

$- 3 f^{6} (g^{1} g^{- 3}) \cdot 2 (7 g^{- 2})$

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

$- 3 f^{6} g^{1 - 3} \cdot 2 (7 g^{- 2})$

Subtract $3$ from $1$ .

$- 3 f^{6} g^{- 2} \cdot 2 (7 g^{- 2})$

Step 4

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

Move $g^{- 2}$ .

$- 3 f^{6} (g^{- 2} g^{- 2}) \cdot 2 \cdot 7$

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

$- 3 f^{6} g^{- 2 - 2} \cdot 2 \cdot 7$

Subtract $2$ from $- 2$ .

$- 3 f^{6} g^{- 4} \cdot 2 \cdot 7$

Step 5

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

$- 3 f^{6} \frac{1}{g^{4}} \cdot 2 \cdot 7$

Step 6

Multiply $- 3 f^{6} \frac{1}{g^{4}}$ .

Combine $- 3$ and $\frac{1}{g^{4}}$ .

$f^{6} \frac{- 3}{g^{4}} \cdot 2 \cdot 7$

Combine $f^{6}$ and $\frac{- 3}{g^{4}}$ .

$\frac{f^{6} \cdot - 3}{g^{4}} \cdot 2 \cdot 7$

Step 7

Simplify the expression.

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

$\frac{- 3 \cdot f^{6}}{g^{4}} \cdot 2 \cdot 7$

Move the negative in front of the fraction.

$- \frac{(3) \cdot f^{6}}{g^{4}} \cdot 2 \cdot 7$

Step 8

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

$- \frac{3 f^{6}}{g^{4}} \cdot 2 \cdot 7$

Step 9

Multiply $- \frac{3 f^{6}}{g^{4}} \cdot 2$ .

Multiply $2$ by $- 1$ .

$- 2 \frac{3 f^{6}}{g^{4}} \cdot 7$

Combine $- 2$ and $\frac{3 f^{6}}{g^{4}}$ .

$\frac{- 2 (3 f^{6})}{g^{4}} \cdot 7$

Multiply $3$ by $- 2$ .

$\frac{- 6 f^{6}}{g^{4}} \cdot 7$

Step 10

Move the negative in front of the fraction.

$- \frac{(6) f^{6}}{g^{4}} \cdot 7$

Step 11

Multiply $- \frac{6 f^{6}}{g^{4}} \cdot 7$ .

Multiply $7$ by $- 1$ .

$- 7 \frac{6 f^{6}}{g^{4}}$

Combine $- 7$ and $\frac{6 f^{6}}{g^{4}}$ .

$\frac{- 7 (6 f^{6})}{g^{4}}$

Multiply $6$ by $- 7$ .

$\frac{- 42 f^{6}}{g^{4}}$

Step 12

Move the negative in front of the fraction.

$- \frac{42 f^{6}}{g^{4}}$

Simplify -3f^2g^-3(2(fg))(7f^3g^-2)

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