Match the expressions that are equivalent.(5 points)

Question

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a. 2^−2 × 2^−3
b. 2^2 / 2^3
c. (2^2)^3
d. 2^8 x 2^-3
e. 2^3 / 2^2

Answer 1

To match the equivalent expressions, we can simplify each expression and determine if they are equal.

1. a. 2^−2 × 2^−3

   • This simplifies to \( 2^{-2 - 3} = 2^{-5} \).

2. b. 2^2 / 2^3

   • This simplifies to \( 2^{2 - 3} = 2^{-1} \).

3. c. (2^2)^3

   • This simplifies to \( 2^{2 \times 3} = 2^6 \).

4. d. 2^8 × 2^−3

   • This simplifies to \( 2^{8 - 3} = 2^{5} \).

5. e. 2^3 / 2^2

   • This simplifies to \( 2^{3 - 2} = 2^{1} \).

So we can summarize the results as follows:

• a. = \( 2^{-5} \)
• b. = \( 2^{-1} \)
• c. = \( 2^{6} \)
• d. = \( 2^{5} \)
• e. = \( 2^{1} \)

Now, we can match equivalent expressions:

• a. 2^−2 × 2^−3 → matches 2^{-5}
• d. 2^8 × 2^−3 → matches 2^5
• c. (2^2)^3 → matches 2^6
• b. 2^2 / 2^3 → matches 2^{-1}
• e. 2^3 / 2^2 → matches 2^1

Putting it all together for matching:

• a matches d
• No matches for b
• c has no match
• e has no match

Please arrange them correctly:

• a with d
• b is unique
• c is unique
• e is unique

Answer 2

ok those where the question these are the answers ok
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