Simplify 4^4(4^-7)(4)

$4^{4} (4^{- 7}) (4)$

Step 1

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

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

$4^{4 - 7} \cdot 4$

Subtract $7$ from $4$ .

$4^{- 3} \cdot 4$

Step 2

Multiply $4^{- 3}$ by $4$ by adding the exponents.

Multiply $4^{- 3}$ by $4$ .

Raise $4$ to the power of $1$ .

$4^{- 3} \cdot 4^{1}$

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

$4^{- 3 + 1}$

Add $- 3$ and $1$ .

$4^{- 2}$

Step 3

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

$\frac{1}{4^{2}}$

Step 4

Raise $4$ to the power of $2$ .

$\frac{1}{16}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{16}$

Decimal Form:

$0.0625$