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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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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