Simplify a^6a^-5q^-9p^5

$a^{6} a^{- 5} q^{- 9} p^{5}$

Step 1

Multiply $a^{6}$ by $a^{- 5}$ by adding the exponents.

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

$a^{6 - 5} q^{- 9} p^{5}$

Subtract $5$ from $6$ .

$a^{1} q^{- 9} p^{5}$

Step 2

Simplify $a^{1} q^{- 9} p^{5}$ .

$a q^{- 9} p^{5}$

Step 3

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

$a \frac{1}{q^{9}} p^{5}$

Step 4

Combine $a$ and $\frac{1}{q^{9}}$ .

$\frac{a}{q^{9}} p^{5}$

Step 5

Combine $\frac{a}{q^{9}}$ and $p^{5}$ .

$\frac{a p^{5}}{q^{9}}$