Move the expressions into the columns to show which expressions are equivalent to the value given at the top of each column. Not all expressions will be used

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.

1/8 --------- 8

options:
2^2 ⋅ 2
2^4/2^-7
2^-3
2^8/2^5
2^0/2^-3
1/2^7 ⋅ 2^-4

Answer 1

To match the expressions with the values of \( \frac{1}{8} \) and \( 8 \), we can simplify each expression:

1. Value = \( \frac{1}{8} \):

   • \( 2^{-3} \) is equal to \( \frac{1}{2^3} = \frac{1}{8} \).

2. Value = \( 8 \):

   • \( 2^{3} \) (since \( 8 = 2^3 \)).
   • \( 2^2 \cdot 2 \) can be simplified to \( 2^{2+1} = 2^3 = 8 \).
   • \( 2^{8}/2^{5} = 2^{8-5} = 2^{3} = 8\).
   • \( 2^{0}/2^{-3} = 2^{0 - (-3)} = 2^{3} = 8 \).
   • \( 1/2^7 \cdot 2^{-4} = 2^{-7-4} = 2^{-11} \) does not equal \( 8 \) or \( \frac{1}{8} \) so it is irrelevant.

Now the assignments can be made as follows:

1. For \( \frac{1}{8} \): Select \( 2^{-3} \)

2. For \( 8 \): Select \( 2^2 \cdot 2 \), \( 2^{8}/2^{5} \), and \( 2^0/2^{-3} \)

So, the final associations are:

• 1/8: \( 2^{-3} \)
• 8: \( 2^2 \cdot 2 \), \( 2^{8}/2^{5} \), \( 2^0/2^{-3} \)

Do not forget to move the corresponding expressions into the correct columns!