Match the expressions that are equivalent.(5 points)

Question

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2^3/2^2
(2^2)^3
2^8×2^−3
2^2/2^3
2^−2×2^−3
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Answer 1

To match the equivalent expressions, we will simplify each expression:

1. \( \frac{2^3}{2^2} = 2^{3-2} = 2^1 = 2 \)

2. \( (2^2)^3 = 2^{2 \cdot 3} = 2^6 \)

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

4. \( \frac{2^2}{2^3} = 2^{2-3} = 2^{-1} = \frac{1}{2} \)

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

Now we have the simplified forms:

1. \( \frac{2^3}{2^2} = 2 \)
2. \( (2^2)^3 = 2^6 \)
3. \( 2^8 \times 2^{-3} = 2^5 \)
4. \( \frac{2^2}{2^3} = \frac{1}{2} \)
5. \( 2^{-2} \times 2^{-3} = 2^{-5} \)

Since you asked to match equivalent expressions, the following relationships are found:

• \( 2^1 \) matches with \( 2 \) (which is itself)
• \( (2^2)^3 = 2^6 \) is unique.
• \( 2^8 \times 2^{-3} = 2^5 \) is unique.
• \( 2^2/2^3 = \frac{1}{2} \) is unique.
• \( 2^{-2} \times 2^{-3} = 2^{-5} \) is unique.

So, there are no equivalent expressions found in this case. If guidance on equivalent matches among these expressions was what you sought, please clarify!