Match the expressions that are equivalent.(5 points)

Question

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

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

Answer 1

Let's evaluate each expression step by step to identify which ones are equivalent to the given responses:

a. \( 2^{-2} \times 2^{-3} = 2^{-2-3} = 2^{-5} = \frac{1}{2^5} = \frac{1}{32} \)

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

c. \( (2^2)^3 = 2^{2 \times 3} = 2^6 = 64 \)

d. \( 2^8 \times 2^{-3} = 2^{8-3} = 2^5 = 32 \)

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

Now we can match the expressions with the responses:

• a. \( 2^{-2} \times 2^{-3} \) matches with \( \frac{1}{32} \)
• b. \( \frac{2^2}{2^3} \) matches with \( \frac{1}{2} \)
• c. \( (2^2)^3 \) matches with \( 64 \)
• d. \( 2^8 \times 2^{-3} \) matches with \( 32 \)
• e. \( \frac{2^3}{2^2} \) matches with \( 2 \)

So the matched responses are:

1. a → \( \frac{1}{32} \)
2. b → \( \frac{1}{2} \)
3. c → \( 64 \)
4. d → \( 32 \)
5. e → \( 2 \)