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:

$$\boxed{{\displaystyle 64}}$$