Nunez Kirk
05/03/2024 · Middle School
Apply the Properties of Integer Exponents to generate equivalent expressions to \( \frac{2^{2}}{2^{-4}} \) with only positive exponents, then solve the expression. Provide the solution as a whole number. (1 point) \( \frac{2^{2}}{2^{4}}= \) Check answer Remaining Attempts : 3
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Tutor-Verified Answer
Step-by-step Solution
To simplify the expression \( \frac{2^{2}}{2^{-4}} \) using the properties of integer exponents, we can apply the quotient rule, which states that \( \frac{a^m}{a^n} = a^{m-n} \).
1. Start with the expression:
\[
\frac{2^{2}}{2^{-4}}
\]
2. Apply the quotient rule:
\[
= 2^{2 - (-4)}
\]
3. Simplify the exponent:
\[
= 2^{2 + 4} = 2^{6}
\]
Now, we can calculate \( 2^{6} \):
\[
2^{6} = 64
\]
Thus, the equivalent expression with only positive exponents is \( 2^{6} \), and the solution to the expression is:
\[
\boxed{64}
\]
Quick Answer
The solution to the expression \( \frac{2^{2}}{2^{-4}} \) is \( 64 \).
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