Simplify (a^-7*a^4)÷(a^-3)

$a^{- 7} \cdot a^{4} \div a^{- 3}$

Rewrite the division as a fraction.

$\frac{a^{- 7} \cdot a^{4}}{a^{- 3}}$

Multiply $a^{- 7}$ by $a^{4}$ by adding the exponents.

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

$\frac{a^{- 7 + 4}}{a^{- 3}}$

Add $- 7$ and $4$ .

$\frac{a^{- 3}}{a^{- 3}}$

Cancel the common factor of $a^{- 3}$ .

Cancel the common factor.

$\frac{a^{- 3}}{a^{- 3}}$

Rewrite the expression.

$1$