Match the expressions that are equivalent.(5 points)

Question

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2−2×2−3
2223
(22)3
28×2−3
2322
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Answer 1

To match the expressions that are equivalent, let's evaluate each expression one by one:

1. Expression: 2 - 2 × 2 - 3

   • This follows the order of operations:
   • = 2 - (2 × 2) - 3
   • = 2 - 4 - 3
   • = 2 - 7
   • = -5

2. Expression: 2223

   • This is not mathematically standard; let's consider it as a sequence of numbers.

3. Expression: (2^2)^3

   • Following the power of a power rule (multiply the exponents):
   • = 2^(2×3)
   • = 2^6
   • = 64

4. Expression: 28 × 2 - 3

   • 28 can be written as 2^3 (since 2^3 = 8):
   • = 8 × 2 - 3
   • = 16 - 3 = 13

5. Expression: 2322

   • Similar to the previous one, this also appears to be a sequence of numbers and not a standard expression.

Now, we notice that:

• The evaluations of the first, third, and fourth expressions do not yield any common results.
• The second and fifth options, being sequences, don’t relate to numerical expressions.

After the evaluations, it appears that none of the expressions given in a conventional manner can be made equivalent.

If you want to match 2 - 2 × 2 - 3 and its numerical evaluation which is -5, that does not seem to align specifically with any of the provided alternatives since they are primarily not equivalently resolvable into numeric values.

However, if we looked deeper into simplifications:

• The expression (2^2)^3 does evaluate to 2^6 or 64, and we can say this becomes the expected - the only directly resolvable numerical expression.

In conclusion, if you meant to match only those expressions to the numbers, please clarify if further assistance is needed or check expressions in detail that provide numeric context.