https://r2.erweima.ai/mathbot/image/17263431793528fv4jmmr.jpg

Let's break down each of the problems in the image step-by-step:

### Problem 1: Simplify the complex fraction
\[
\frac{\frac{6}{7}}{\frac{16}{49}}
\]
- To simplify, we multiply the numerator by the reciprocal of the denominator:
\[
\frac{6}{7} \div \frac{16}{49} = \frac{6}{7} \times \frac{49}{16} = \frac{6 \times 49}{7 \times 16} = \frac{294}{112}
\]
- Simplifying \(\frac{294}{112}\), divide both numerator and denominator by 14:
\[
\frac{294 \div 14}{112 \div 14} = \frac{21}{8}
\]
So, the simplified fraction is:
\[
\frac{21}{8}
\]

### Problem 2: Find the value of the expression
\[
3^2 + 2(1 + 5) - 2
\]
- First, evaluate the exponent:
\[
3^2 = 9
\]
- Next, simplify inside the parentheses:
\[
1 + 5 = 6
\]
- Now, multiply:
\[
2 \times 6 = 12
\]
- Finally, complete the expression:
\[
9 + 12 - 2 = 19
\]
So, the value is:
\[
19
\]

### Problem 3: Find the square root of \(\sqrt{196}\)
- The square root of 196 is:
\[
\sqrt{196} = 14
\]

### Problem 4: Simplify \(\sqrt{12}\)
- Factor 12 as \(4 \times 3\), and take the square root of 4:
\[
\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}
\]
So, the simplified form is:
\[
2\sqrt{3}
\]

---

Let me know if you'd like more details or further clarifications on any of these problems!

Here are five related questions:
1. How do you simplify a complex fraction involving variables?
2. What are the rules for simplifying square roots of non-perfect squares?
3. How do you simplify expressions with exponents and multiple operations?
4. What is the square root of a negative number (e.g., \(\sqrt{-16}\))?
5. How can you find the cube root of a number (e.g., \(\sqrt[3]{27}\))?

**Tip**: When simplifying fractions, always look for common factors between the numerator and the denominator to reduce the fraction quickly!

Learn how to simplify a complex fraction, evaluate expressions with exponents, and calculate square roots with a step-by-step solution. This problem is suitable for students in Grades 6-8, covering key topics like fractions, exponents, and square roots.

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