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 solutions to the problems. 1) Simplify 20^100 ÷ 20^100. Step 1: Apply the division rule for exponents, a^m ÷ a^n = a^m-n. 20^100 ÷ 20^100 = 20^100-100 Step 2: Simplify the exponent. 20^100-100 = 20^0 Step 3: Apply the rule a^0 = 1 for any non-zero base a. 20^0 = 1 The simplified expression is 1. 2) Simplify (x^3)/(2x^3). Step 1: Separate the coefficient and variable terms. (x^3)/(2x^3) = (1)/(2) × (x^3)/(x^3) Step 2: Simplify the variable term using the rule a^m ÷ a^m = 1. (x^3)/(x^3) = x^3-3 = x^0 = 1 Step 3: Multiply the simplified parts. (1)/(2) × 1 = (1)/(2) The simplified expression is (1)/(2). 3) Simplify (-2xyz)^0. Step 1: Apply the rule a^0 = 1 for any non-zero base a. Since the entire expression (-2xyz) is raised to the power of 0, the result is 1. (-2xyz)^0 = 1 The simplified expression is 1. 4) Simplify ((2a^5b^3)^3 (2a^2b^4)^2)/(32a^19)b^17. Step 1: Simplify the first term in the numerator, (2a^5b^3)^3. Apply (xy)^n = x^n y^n and (x^m)^n = x^mn. (2a^5b^3)^3 = 2^3 (a^5)^3 (b^3)^3 = 8a^15b^9 Step 2: Simplify the second term in the numerator, (2a^2b^4)^2. Apply (xy)^n = x^n y^n and (x^m)^n = x^mn. (2a^2b^4)^2 = 2^2 (a^2)^2 (b^4)^2 = 4a^4b^8 Step 3: Multiply the simplified terms in the numerator. (8a^15b^9)(4a^4b^8) = (8 × 4)(a^15a^4)(b^9b^8) Apply a^m a^n = a^m+n. 32a^15+4b^9+8 = 32a^19b^17 Step 4: Substitute the simplified numerator back into the original expression. 32a^19b^1732a^19b^17 Step 5: Simplify the entire fraction. Since the numerator and denominator are identical, the expression simplifies to 1. 32a^19b^1732a^19b^17 = 1 The simplified expression is 1. 5) Simplify (2^12a^2vfq^2w^2ercsd^9f^10q^3)^0. Step 1: Apply the rule a^0 = 1 for any non-zero base a. Since the entire fraction inside the parentheses is raised to the power of 0, the result is 1. (2^12a^2vfq^2w^2ercsd^9f^10q^3)^0 = 1 The simplified expression is 1. That's 2 down. 3 left today — send the next one.