Match the expressions that are equivalent.(5 points)

Question

Put responses in the correct input to answer the question.
1. 2^3/2^2:
2. 2^−2 × 2^−3:
3. 2^8 × 2^−3:
4. (2^2)^3:
5. 2^2/2^3:

Answer 1

Let's evaluate each expression to find the equivalent ones:

1. $\frac{2^3}{2^2}=2^{3-2}=2^1=2$

2. $2^{-2}\times 2^{-3}=2^{-2+(-3)}=2^{-5}$

3. $2^8\times 2^{-3}=2^{8+(-3)}=2^5$

4. $(2^2{)}^3=2^{2\times 3}=2^6$

5. $\frac{2^2}{2^3}=2^{2-3}=2^{-1}=\frac{1}{2}$

Now we can summarize the results:

1. $2$
2. $2^{-5}$
3. $2^5$
4. $2^6$
5. $\frac{1}{2}$

The equivalent expressions are:

• Expression 1 ($2^3/2^2$) is equivalent to $2$.
• Expression 3 ($2^8\times 2^{-3}$) is equivalent to $2^5$.
• Expression 4 ($(2^2{)}^3$) is equivalent to $2^6$.
• Expression 5 ($2^2/2^3$) is equivalent to $\frac{1}{2}$.
• Expression 2 ($2^{-2}\times 2^{-3}$) is equivalent to $2^{-5}$.

So we can group them as follows:

• $2^3/2^2\equiv 2$
• $2^8\times 2^{-3}\equiv 2^5$
• $(2^2{)}^3\equiv 2^6$
• $2^2/2^3\equiv \frac{1}{2}$
• $2^{-2}\times 2^{-3}\equiv 2^{-5}$

This provides a good framing for grouping the outputs. However, since no specific equivalent expressions were required, there's no explicit matching required in a traditional sense—each expression has its unique outcome when simplified. If you need a direct answer based on equivalency or matching, please specify how you prefer it formatted!