# How do you simplify (4^0*4^-4)/4^0 and write it using only positive exponents?

Oct 2, 2016

Simplify each term, then solve.

#### Explanation:

The key thing we need to know is that a base with an exponent of 0 equals 1. This means that the two ${4}^{0}$s equal 1. Using this rule, we can simplify this expression:

$\frac{{4}^{0} \cdot {4}^{-} 4}{4} ^ 0 = \frac{1 \cdot {4}^{-} 4}{1} = {4}^{-} 4$

Now that we've simplified the expression a bit, we now have to simplify it a bit more. You may recall that ${x}^{-} y = \frac{1}{x} ^ y$. Using this rule, we can get our answer:

${4}^{-} 4 = \frac{1}{4} ^ 4 = \frac{1}{256}$