Apply the Properties of Integer Exponents to generate equivalent expressions to 2(2)/2(−4)

Question

with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
222−4=

Answer 1

To simplify the expression \( \frac{2^2}{2^{-4}} \) using the properties of integer exponents, we can apply the quotient property of exponents, which states:

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

In this case, let \( a = 2 \), \( m = 2 \), and \( n = -4 \). Therefore, we can rewrite the expression as:

\[ \frac{2^2}{2^{-4}} = 2^{2 - (-4)} = 2^{2 + 4} = 2^6 \]

Now, we can express \( 2^6 \) as a whole number:

\[ 2^6 = 64 \]

Thus, the solution to the expression \( \frac{2^2}{2^{-4}} \) is:

\[ \boxed{64} \]