Apply All Exponent Rules Practice

Question

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Question
Apply the Properties of Integer Exponents to generate equivalent expressions to 2^2/2^−4
with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
2^2/2^−4=

Answer 1

To apply the properties of integer exponents to the expression \( \frac{2^2}{2^{-4}} \), we will use the quotient rule of exponents, which states that:

\[ \frac{a^m}{a^n} = a^{m-n} \]

Applying this to our expression:

\[ \frac{2^2}{2^{-4}} = 2^{2 - (-4)} \]

This simplifies to:

\[ 2^{2 + 4} = 2^6 \]

Now, we need to solve for \( 2^6 \):

\[ 2^6 = 64 \]

So the final answer is:

\[ \frac{2^2}{2^{-4}} = 64 \]