Question

Match the expressions that are equivalent.(5 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
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

ok those where the question these are the answers ok
1/32
32
64
2
1/2
1/64

Answer 2

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