Which of the following option is not correct?

Options

A. `16^(2)÷4^(3) =2^(2)`
B. `3^(2) xx 27 = 3^(5)`
C. `[(-2)^(2)]^(m) = 4^(m)`
D. `4^(0) + 4^(1) +4^(2) = 20`

Answer

To determine which of the given options is not correct, we will evaluate each option step by step.

### Step 1: Evaluate Option 1
**Option 1:** \( 16^2 \div 4^3 = 2^2 \)

1. Calculate \( 16^2 \):
\[ 16^2 = 256 \]

2. Calculate \( 4^3 \):
\[ 4^3 = 64 \]

3. Divide \( 256 \) by \( 64 \):
\[ 256 \div 64 = 4 \]

4. Calculate \( 2^2 \):
\[ 2^2 = 4 \]

5. Since \( 4 = 4 \), **Option 1 is correct.**

### Step 2: Evaluate Option 2
**Option 2:** \( 3^2 \times 27 = 3^2 \times 27^3 \)

1. Rewrite \( 27 \) as \( 3^3 \):
\[ 27 = 3^3 \]

2. Substitute \( 27 \) into the equation:
\[ 3^2 \times (3^3)^3 \]

3. Apply the power of a power rule:
\[ (3^3)^3 = 3^{3 \times 3} = 3^9 \]

4. Now, we have:
\[ 3^2 \times 3^9 \]

5. Add the exponents (since the bases are the same):
\[ 3^{2 + 9} = 3^{11} \]

6. Therefore, **Option 2 is correct.**

### Step 3: Evaluate Option 3
**Option 3:** \( (-2)^2 \) raised to \( m \)

1. Calculate \( (-2)^2 \):
\[ (-2)^2 = 4 \]

2. Raise \( 4 \) to the power of \( m \):
\[ 4^m \]

3. Thus, **Option 3 is correct.**

### Step 4: Evaluate Option 4
**Option 4:** \( 4^0 + 4^1 + 4^2 \)

1. Calculate \( 4^0 \):
\[ 4^0 = 1 \]

2. Calculate \( 4^1 \):
\[ 4^1 = 4 \]

3. Calculate \( 4^2 \):
\[ 4^2 = 16 \]

4. Add these values together:
\[ 1 + 4 + 16 = 21 \]

5. The statement claims this equals 20, which is incorrect. Thus, **Option 4 is not correct.**

### Conclusion
The option that is not correct is **Option 4**.

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