Question

Match the exponent form to the correct standard form.(7 points)
2(4)
−8(2)
2(−3)
(−4)(2)
2(3) ⋅ 3(2)
(4/5)(2)
(2/3)(3)

responses
8/27
72
1/8
-64
16
16/25
8
8/10
6/9
7776

Answer 1

Let's calculate each exponent form and match it with the correct standard form:

1. **2(4)**: This is \(2^4 = 16\).

2. **−8(2)**: This is \(-8^2 = -64\).

3. **2(−3)**: This is \(2^{-3} = \frac{1}{2^3} = \frac{1}{8}\).

4. **(−4)(2)**: This is \((-4)^2 = 16\).

5. **2(3) ⋅ 3(2)**: This is \(2^3 \cdot 3^2 = 8 \cdot 9 = 72\).

6. **(4/5)(2)**: This is \((\frac{4}{5})^2 = \frac{16}{25}\).

7. **(2/3)(3)**: This is \((\frac{2}{3})^3 = \frac{8}{27}\).

Now, matching them:

- **16**: from \(2(4)\) or \((-4)(2)\)
- **-64**: from \(-8(2)\)
- **1/8**: from \(2(−3)\)
- **72**: from \(2(3) \cdot 3(2)\)
- **16/25**: from \((4/5)(2)\)
- **8/27**: from \((2/3)(3)\)

Here’s the summary of the matches:

- \(2(4) \rightarrow 16\)
- \(-8(2) \rightarrow -64\)
- \(2(−3) \rightarrow \frac{1}{8}\)
- \((−4)(2) \rightarrow 16\)
- \(2(3) \cdot 3(2) \rightarrow 72\)
- \((4/5)(2) \rightarrow \frac{16}{25}\)
- \((2/3)(3) \rightarrow \frac{8}{27}\)