QUESTION 6 [EXPONENTS] Calculate the values of the following: 6.1 2/60, 6.2 53 x 54, 6.3 85 + 83, 6.4 Show by means of calculations that 25 is bigger than 52.

Here are the solutions to the questions: QUESTION 6 [EXPONENTS] 6.1. Step 1: Evaluate the term with the exponent. Any non-zero number raised to the power of 0 is 1. 6^0 = 1 Step 2: Substitute this value back into the expression and simplify. (2)/(1) = 2 The value is 2. 6.2. Step 1: Apply the rule for multiplying exponents with the same base: a^m × a^n = a^m+n. 5^3 × 5^4 = 5^3+4 Step 2: Add the exponents and calculate the final value. 5^7 = 78125 The value is 78125. 6.3. Step 1: Apply the rule for dividing exponents with the same base: a^m ÷ a^n = a^m-n. 8^5 ÷ 8^3 = 8^5-3 Step 2: Subtract the exponents and calculate the final value. 8^2 = 64 The value is 64. 6.4. Step 1: Calculate the value of 2^5. 2^5 = 2 × 2 × 2 × 2 × 2 = 32 Step 2: Calculate the value of 5^2. 5^2 = 5 × 5 = 25 Step 3: Compare the two values. 32 > 25 Therefore, 2^5 is bigger than 5^2. QUESTION 7 [NUMERIC AND GEOMETRIC PATTERNS] 7.1.1. Step 1: Find the common difference between consecutive terms. -5 - (-2) = -3 -8 - (-5) = -3 -11 - (-8) = -3 Step 2: Add the common difference to the last given term to find the next term. -11 + (-3) = -14 The next term is -14. 7.1.2. Step 1: Identify the first term (a) and the common difference (d). a = -2 d = -3 Step 2: Use the general formula for an arithmetic sequence, T_n = a + (n-1)d. T_n = -2 + (n-1)(-3) Step 3: Simplify the expression to find the general rule. T_n = -2 - 3n + 3 T_n = 1 - 3n The general rule is T_n = 1 - 3n. 7.1.3. Step 1: Use the general rule T_n = 1 - 3n found in 7.1.2. Step 2: Substitute n = 50 into the rule to find the 50th term. T_50 = 1 - 3(50) Step 3: Perform the multiplication and subtraction. T_50 = 1 - 150 T_50 = -149 The 50th term is -149. 3 done, 2 left today. You're making progress.