This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Ona💘💘💋💞, let's knock this out. 2. Simplify and test your answer. 2.a) c^2 × c^4 = Step 1: Simplify the expression using the rule a^m × a^n = a^m+n. c^2 × c^4 = c^2+4 = c^6 Step 2: Test with c=2. Original: 2^2 × 2^4 = 4 × 16 = 64 Simplified: 2^6 = 64 The simplified expression is c^6. 2.b) m^4 × m^5 = Step 1: Simplify the expression. m^4 × m^5 = m^4+5 = m^9 Step 2: Test with m=3. Original: 3^4 × 3^5 = 81 × 243 = 19683 Simplified: 3^9 = 19683 The simplified expression is m^9. 2.c) p^7 × p^3 = Step 1: Simplify the expression. p^7 × p^3 = p^7+3 = p^10 Step 2: Test with p=2. Original: 2^7 × 2^3 = 128 × 8 = 1024 Simplified: 2^10 = 1024 The simplified expression is p^10. 2.d) q^3 × q^7 = Step 1: Simplify the expression. q^3 × q^7 = q^3+7 = q^10 Step 2: Test with q=3. Original: 3^3 × 3^7 = 27 × 2187 = 59049 Simplified: 3^10 = 59049 The simplified expression is q^10. 2.e) x^5 × x^8 = Step 1: Simplify the expression. x^5 × x^8 = x^5+8 = x^13 Step 2: Test with x=4. Original: 4^5 × 4^8 = 1024 × 65536 = 67108864 Simplified: 4^13 = 67108864 The simplified expression is x^13. 2.f) s^9 × s^2 = Step 1: Simplify the expression. s^9 × s^2 = s^9+2 = s^11 Step 2: Test with s=5. Original: 5^9 × 5^2 = 1953125 × 25 = 48828125 Simplified: 5^11 = 48828125 The simplified expression is s^11. 3. Why can we say: a^m × a^n = a^m+n? Give three examples. We can say a^m × a^n = a^m+n because when you multiply exponential terms that have the same base, you are essentially counting the total number of times that base is multiplied by itself. The exponent m indicates a is multiplied m times, and n indicates a is multiplied n times. When you multiply these two expressions, you combine all those multiplications, resulting in a being multiplied a total of m+n times. Here are three examples: a. 2^3 × 2^2 This means (2 × 2 × 2) × (2 × 2). Counting all the 2s being multiplied, we have 2 × 2 × 2 × 2 × 2, which is 2^5. Using the rule, 2^3+2 = 2^5. b. x^4 × x^1 This means (x × x × x × x) × (x). Counting all the xs being multiplied, we have x × x × x × x × x, which is x^5. Using the rule, x^4+1 = x^5. c. y^2 × y^3 This means (y × y) × (y × y × y). Counting all the ys being multiplied, we have y × y × y × y × y, which is y^5. Using the rule, y^2+3 = y^5. Drop the next question!