Match the expressions that are equivalent.(5 points)

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:

1 answer

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

  1. 2322=232=21=2

  2. 22×23=22+(3)=25

  3. 28×23=28+(3)=25

  4. (22)3=22×3=26

  5. 2223=223=21=12

Now we can summarize the results:

  1. 2
  2. 25
  3. 25
  4. 26
  5. 12

The equivalent expressions are:

  • Expression 1 (23/22) is equivalent to 2.
  • Expression 3 (28×23) is equivalent to 25.
  • Expression 4 ((22)3) is equivalent to 26.
  • Expression 5 (22/23) is equivalent to 12.
  • Expression 2 (22×23) is equivalent to 25.

So we can group them as follows:

  • 23/222
  • 28×2325
  • (22)326
  • 22/2312
  • 22×2325

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!