Simplify (4^5*4^-7)÷(4^-2)

$4^{5} \cdot 4^{- 7} \div 4^{- 2}$

Step 1

Rewrite the division as a fraction.

$\frac{4^{5} \cdot 4^{- 7}}{4^{- 2}}$

Step 2

Multiply $4^{5}$ by $4^{- 7}$ by adding the exponents.

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

$\frac{4^{5 - 7}}{4^{- 2}}$

Subtract $7$ from $5$ .

$\frac{4^{- 2}}{4^{- 2}}$

Step 3

Cancel the common factor of $4^{- 2}$ .

Cancel the common factor.

$\frac{4^{- 2}}{4^{- 2}}$

Rewrite the expression.

$1$