Question

Which expression is equal to 4 ^ 5 * 4 ^ - 7 / (4 ^ - 2)

Answer 1

To simplify the expression \( 4^5 \cdot 4^{-7} / 4^{-2} \), we can use the properties of exponents.

First, recall that when multiplying like bases, we add the exponents:
\[
4^5 \cdot 4^{-7} = 4^{5 + (-7)} = 4^{-2}
\]

Now, our expression becomes:
\[
\frac{4^{-2}}{4^{-2}}
\]

Next, when dividing like bases, we subtract the exponents:
\[
\frac{4^{-2}}{4^{-2}} = 4^{-2 - (-2)} = 4^{0}
\]

Since any non-zero number raised to the power of 0 is 1, we get:
\[
4^0 = 1
\]

Thus, the expression \( 4^5 \cdot 4^{-7} / 4^{-2} \) is equal to \( \boxed{1} \).