Which of the following is incorrect ?

Options

A. `3^(2)xx 4^(2) gt 2^(3)xx 2^(4)`
B. `7^(2) lt 2^(7)`
C. `(285)^(0) lt (-3)^(2)`
D. `(-1)^(27) gt (-1)^(14)`

Answer

To determine which of the given inequalities is incorrect, we will analyze each option step by step.

### Step 1: Analyze the first inequality
**Inequality:** \( 3 \times 3 < 4 \times 4 \times 4 \)

**Calculation:**
- Left side: \( 3 \times 3 = 9 \)
- Right side: \( 4 \times 4 \times 4 = 64 \)

**Comparison:**
- \( 9 < 64 \) is true.

### Step 2: Analyze the second inequality
**Inequality:** \( 7^2 < 2^7 \)

**Calculation:**
- Left side: \( 7^2 = 49 \)
- Right side: \( 2^7 = 128 \)

**Comparison:**
- \( 49 < 128 \) is true.

### Step 3: Analyze the third inequality
**Inequality:** \( 285^0 < 2^{-3} \)

**Calculation:**
- Left side: \( 285^0 = 1 \) (Any non-zero number raised to the power of 0 is 1)
- Right side: \( 2^{-3} = \frac{1}{2^3} = \frac{1}{8} \)

**Comparison:**
- \( 1 < \frac{1}{8} \) is false (since 1 is greater than \( \frac{1}{8} \)).

### Step 4: Analyze the fourth inequality
**Inequality:** \( (-1)^{27} > 1^{14} \)

**Calculation:**
- Left side: \( (-1)^{27} = -1 \) (since 27 is odd)
- Right side: \( 1^{14} = 1 \)

**Comparison:**
- \( -1 > 1 \) is false (since -1 is less than 1).

### Conclusion
The incorrect inequalities are:
1. \( 285^0 < 2^{-3} \) (which is false)
2. \( (-1)^{27} > 1^{14} \) (which is also false)

However, since the question asks for one incorrect option, we can conclude that the first incorrect inequality we found is \( 285^0 < 2^{-3} \).

### Final Answer
The incorrect inequality is: **\( 285^0 < 2^{-3} \)**.

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