Simplify (7p^-3)(-6p^5q^-2)

$(7 p^{- 3}) (- 6 p^{5} q^{- 2})$

Step 1

Multiply $p^{- 3}$ by $p^{5}$ by adding the exponents.

Move $p^{5}$ .

$7 (p^{5} p^{- 3}) (- 6 q^{- 2})$

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

$7 p^{5 - 3} (- 6 q^{- 2})$

Subtract $3$ from $5$ .

$7 p^{2} (- 6 q^{- 2})$

Step 2

Rewrite using the commutative property of multiplication.

$7 \cdot - 6 p^{2} q^{- 2}$

Step 3

Multiply $7$ by $- 6$ .

$- 42 p^{2} q^{- 2}$

Step 4

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

$- 42 p^{2} \frac{1}{q^{2}}$

Step 5

Multiply $- 42 p^{2} \frac{1}{q^{2}}$ .

Combine $- 42$ and $\frac{1}{q^{2}}$ .

$p^{2} \frac{- 42}{q^{2}}$

Combine $p^{2}$ and $\frac{- 42}{q^{2}}$ .

$\frac{p^{2} \cdot - 42}{q^{2}}$

Step 6

Move $- 42$ to the left of $p^{2}$ .

$\frac{- 42 \cdot p^{2}}{q^{2}}$

Step 7

Move the negative in front of the fraction.

$- \frac{42 p^{2}}{q^{2}}$