Let's break down and solve the expression step by step:

Given expression:  
\[ 4 \times 7^0 - \left(\frac{3}{4} - \frac{1}{2}\right)^2 - \frac{12}{4} \]

1. **Evaluate \( 7^0 \):**
   \[ 7^0 = 1 \]

2. **Multiply by 4:**
   \[ 4 \times 1 = 4 \]

3. **Calculate \( \frac{3}{4} - \frac{1}{2} \):**
   Convert \( \frac{1}{2} \) to \( \frac{2}{4} \):
   \[ \frac{3}{4} - \frac{2}{4} = \frac{1}{4} \]

4. **Square \( \frac{1}{4} \):**
   \[ \left(\frac{1}{4}\right)^2 = \frac{1}{16} \]

5. **Divide 12 by 4:**
   \[ \frac{12}{4} = 3 \]

Now, substitute all these values back into the expression:
\[ 4 - \frac{1}{16} - 3 \]

6. **Simplify the expression:**
   \[ 4 - 3 - \frac{1}{16} = 1 - \frac{1}{16} \]

7. **Final subtraction:**
   \[ 1 - \frac{1}{16} = \frac{16}{16} - \frac{1}{16} = \frac{15}{16} \]

The final result is:

\[
\frac{15}{16}
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How do you simplify expressions with exponents and fractions?
2. What is the significance of \( x^0 = 1 \) for any non-zero x?
3. How do you perform subtraction and addition with fractions having different denominators?
4. Can you explain the steps for squaring a fraction?
5. What is the difference between a fraction and a decimal representation?

**Tip:** When working with fractions, it's often helpful to convert all fractions to have a common denominator before performing addition or subtraction.

Explore a step-by-step solution to the expression 4x7⁰ - (3/4 - 1/2)² - 12:4, involving exponentiation, fractions, and order of operations. This problem is ideal for students in Grades 5-7 and covers essential mathematical concepts and formulas.

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