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)

Answer 1

To generate equivalent expressions with only positive exponents, we can use the property of exponents that states:
\[a^{-b} = \frac{1}{a^b}\]

Applying this property to the expression \(2^{2}/2^{-4}\), we can rewrite it as:
\[2^2 / 2^{-4} = 2^2 \times (2^{-4})^{-1} = 2^2 \times 2^{4} = 2^{2+4} = 2^{6}\]

Now, we can solve the expression:
\[2^{6} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64\]

So, the solution to the expression is 64.