Question
Apply the Properties of Integer Exponents to generate equivalent expressions to 2 raised to the 2 power/2 raised to the −4 power with only positive exponents, then solve the expression. Provide the solution as a whole number.
Answers
GPT-4o mini
To simplify the expression \( \frac{2^2}{2^{-4}} \) using the properties of integer exponents, we can use the quotient of powers property, which states that:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, we can apply this property:
\[
\frac{2^2}{2^{-4}} = 2^{2 - (-4)} = 2^{2 + 4} = 2^6
\]
Now, we can calculate \( 2^6 \):
\[
2^6 = 64
\]
Thus, the equivalent expression simplifies to a whole number, which is
\[
\boxed{64}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, we can apply this property:
\[
\frac{2^2}{2^{-4}} = 2^{2 - (-4)} = 2^{2 + 4} = 2^6
\]
Now, we can calculate \( 2^6 \):
\[
2^6 = 64
\]
Thus, the equivalent expression simplifies to a whole number, which is
\[
\boxed{64}
\]