Solve the math problems written on the board.

Let's solve the math problems step-by-step.

1. Problem 1: 8 - 6c - 6 + c

   Combine like terms (constants and terms with 'c'):

   $$8 - 6 - 6c + c = 2 - 5c$$

   Answer: 2 - 5c

2. Problem 2: 5x³y⁴ * (-4xy⁵)

   Multiply the coefficients and add the exponents of like variables:

   $$(5 * -4) * (x^3 * x) * (y^4 * y^5) = -20 * x^{3+1} * y^{4+5} = -20x^4y^9$$

   Answer: -20x⁴y⁹

3. Problem 3: (5x⁶y⁸)²

   Apply the power to each factor inside the parentheses:

   $$5^2 * (x^6)^2 * (y^8)^2 = 25 * x^{6*2} * y^{8*2} = 25x^{12}y^{16}$$

   Answer: 25x¹²y¹⁶

4. Problem 4a: (6¹⁵ * 6⁷) / 6¹⁹

   First, simplify the numerator by adding the exponents:

   $$6^{15} * 6^{7} = 6^{15+7} = 6^{22}$$

   Now, divide by 6¹⁹ by subtracting the exponents:

   $$\frac{6^{22}}{6^{19}} = 6^{22-19} = 6^3$$

   Finally, calculate 6³:

   $$6^3 = 6 * 6 * 6 = 216$$

   Answer: 216

5. Problem 4b: (9 * 3⁴) / 27²

   Rewrite 9 and 27 as powers of 3:

   $$9 = 3^2$$

   $$27 = 3^3$$

   So, 27² = (3³)² = 3⁶

   Now substitute these into the original expression:

   $$\frac{3^2 * 3^4}{3^6} = \frac{3^{2+4}}{3^6} = \frac{3^6}{3^6} = 1$$

   Answer: 1