Simplify (a^7a^-22)/(a^-10)

$\frac{a^{7} a^{- 22}}{a^{- 10}}$

Step 1

Multiply $a^{7}$ by $a^{- 22}$ by adding the exponents.

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

$\frac{a^{7 - 22}}{a^{- 10}}$

Subtract $22$ from $7$ .

$\frac{a^{- 15}}{a^{- 10}}$

Step 2

Move $a^{- 15}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{a^{- 10} a^{15}}$

Step 3

Multiply $a^{- 10}$ by $a^{15}$ by adding the exponents.

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

$\frac{1}{a^{- 10 + 15}}$

Add $- 10$ and $15$ .

$\frac{1}{a^{5}}$