Match the expressions that are equivalent.(5 points)

Question

2^8 × 2^−3

2^2 over 2^3

2^−2 × 2^−3

2^3 over 2^2

(2^2)^3

options:

32
1 over 32
2
64
1 over 62
1 over 2

Answer 1

Let's evaluate each expression to find the equivalent ones.

1. \(2^8 \times 2^{-3}\): \[ 2^8 \times 2^{-3} = 2^{8 - 3} = 2^5 = 32 \]

2. \(\frac{2^2}{2^3}\): \[ \frac{2^2}{2^3} = 2^{2 - 3} = 2^{-1} = \frac{1}{2} \]

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

4. \(\frac{2^3}{2^2}\): \[ \frac{2^3}{2^2} = 2^{3 - 2} = 2^1 = 2 \]

5. \((2^2)^3\): \[ (2^2)^3 = 2^{2 \times 3} = 2^6 = 64 \]

Now, we can match the results:

1. \(2^8 \times 2^{-3} = 32\)
2. \(\frac{2^2}{2^3} = \frac{1}{2}\)
3. \(2^{-2} \times 2^{-3} = \frac{1}{32}\)
4. \(\frac{2^3}{2^2} = 2\)
5. \((2^2)^3 = 64\)

The pairs are as follows:

• \(2^8 \times 2^{-3} \) -> \(32\)
• \(\frac{2^2}{2^3} \) -> \(\frac{1}{2}\)
• \(2^{-2} \times 2^{-3} \) -> \(\frac{1}{32}\)
• \(\frac{2^3}{2^2} \) -> \(2\)
• \((2^2)^3 \) -> \(64\)

So the matches are:

1. \(32\)
2. \(\frac{1}{2}\)
3. \(\frac{1}{32}\)
4. \(2\)
5. \(64\)