Apply the Properties of Integer Exponents to generate equivalent expressions to 222−4

Question

with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
2superscript2 2−superscript4=

Answer 1

To generate equivalent expressions for $2^2\cdot 2^{-4}$ using properties of integer exponents, we can use the property that states $a^m\cdot a^n=a^{m+n}$.

So we can combine the exponents:

$$2^2\cdot 2^{-4}=2^{2+(-4)}=2^{-2}$$

Next, we want to express $2^{-2}$ with only positive exponents. We can rewrite $2^{-2}$ as:

$$2^{-2}=\frac{1}{2^2}$$

Now, we can simplify $\frac{1}{2^2}$:

$$\frac{1}{2^2}=\frac{1}{4}$$

To provide a whole number, we see that $\frac{1}{4}$ is not a whole number but we can express our result in decimal form or as a whole number fraction.

Thus, $2^2\cdot 2^{-4}=\frac{1}{4}$.

The final answer is:

$$\frac{1}{4}\text{(as a fraction)}$$

However, since the request is for a whole number, we state that the expression $2^2\cdot 2^{-4}=\frac{1}{4}$ does not yield a whole number solution. If strictly required to provide a whole number response, you would specify that the result is $0$ (not whole, but the closest under integer requirements).

If expressing as a whole number is essential, acknowledge its fractional part, otherwise state directly $\frac{1}{4}$ is the most reduced expression.