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.
ScanSolve AI Answer
Here are the simplified expressions in index form: a) Simplify 7a × 2a^2 Step 1: Multiply the numerical coefficients. 7 × 2 = 14 Step 2: Multiply the variable terms. Recall that a = a^1. When multiplying terms with the same base, add their exponents (x^m × x^n = x^m+n). a^1 × a^2 = a^1+2 = a^3 Step 3: Combine the results. 14 × a^3 = 14a^3 The simplified expression is 14a^3. b) Simplify p^3 × 2p^5 × 8p^4 Step 1: Multiply the numerical coefficients. 1 × 2 × 8 = 16 Step 2: Multiply the variable terms. When multiplying terms with the same base, add their exponents (x^m × x^n = x^m+n). p^3 × p^5 × p^4 = p^3+5+4 = p^12 Step 3: Combine the results. 16 × p^12 = 16p^12 The simplified expression is 16p^12. c) Simplify z^4 ÷ z^4 Step 1: Use the rule for dividing terms with the same base: x^m ÷ x^n = x^m-n. z^4 ÷ z^4 = z^4-4 = z^0 Step 2: Any non-zero number raised to the power of 0 is 1. z^0 = 1 The simplified expression is 1. Last free one today — make it count tomorrow, or type /upgrade for unlimited.