Alright, let's solve these math problems step-by-step:
### 3. Evaluate: [tex]\(-6 + 3(9 - 7)\)[/tex]
1. Start with the expression: [tex]\(-6 + 3(9 - 7)\)[/tex].
2. Solve the expression inside the parentheses first: [tex]\(9 - 7 = 2\)[/tex].
3. Then, the expression becomes: [tex]\(-6 + 3 \times 2\)[/tex].
4. Multiply: [tex]\(3 \times 2 = 6\)[/tex].
5. Finally, add: [tex]\(-6 + 6 = 0\)[/tex].
So, [tex]\(-6 + 3(9 - 7) = 0\)[/tex].
### 4. Evaluate: [tex]\(-8 \div (1 + 3) - 1\)[/tex]
1. Start with the expression: [tex]\(-8 \div (1 + 3) - 1\)[/tex].
2. Solve the expression inside the parentheses first: [tex]\(1 + 3 = 4\)[/tex].
3. Then, the expression becomes: [tex]\(-8 \div 4 - 1\)[/tex].
4. Perform the division: [tex]\(-8 \div 4 = -2\)[/tex].
5. Finally, subtract: [tex]\(-2 - 1 = -3\)[/tex].
So, [tex]\(-8 \div (1 + 3) - 1 = -3\)[/tex].
### 5. Evaluate: [tex]\(-7 + 2 \cdot 6^2 - 8\)[/tex]
1. Start with the expression: [tex]\(-7 + 2 \cdot 6^2 - 8\)[/tex].
2. Evaluate the exponent first: [tex]\(6^2 = 36\)[/tex].
3. Then, the expression becomes: [tex]\(-7 + 2 \cdot 36 - 8\)[/tex].
4. Multiply: [tex]\(2 \times 36 = 72\)[/tex].
5. Then, the expression becomes: [tex]\(-7 + 72 - 8\)[/tex].
6. Perform the addition and subtraction from left to right:
- First: [tex]\(-7 + 72 = 65\)[/tex].
- Then: [tex]\(65 - 8 = 57\)[/tex].
So, [tex]\(-7 + 2 \cdot 6^2 - 8 = 57\)[/tex].
### 6. Simplify the fraction: [tex]\(\frac{10}{25}\)[/tex]
1. Start with the fraction [tex]\(\frac{10}{25}\)[/tex].
2. Find the greatest common divisor (GCD) of the numerator (10) and the denominator (25). The GCD of 10 and 25 is 5.
3. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{10 \div 5}{25 \div 5} = \frac{2}{5}
\][/tex]
So, the simplified fraction [tex]\(\frac{10}{25}\)[/tex] is [tex]\(\frac{2}{5}\)[/tex].
### Summary
1. [tex]\(-6 + 3(9 - 7) = 0\)[/tex]
2. [tex]\(-8 \div (1 + 3) - 1 = -3\)[/tex]
3. [tex]\(-7 + 2 \cdot 6^2 - 8 = 57\)[/tex]
4. [tex]\(\frac{10}{25} = \frac{2}{5}\)[/tex]
