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
You're on a roll — Here are the solutions to the questions: 1. Simplify the expression (30x^4)/(3x^-2) Working out: Step 1: Divide the numerical coefficients. (30)/(3) = 10 Step 2: Apply the division rule for exponents, which states that (a^m)/(a^n) = a^m-n. (x^4)/(x^-2) = x^4 - (-2) = x^4+2 = x^6 Step 3: Combine the simplified numerical and variable terms. 10x^6 Answer: 10x^6 2. Simplify ((x^3)/(2^2))^-2 Working out: Step 1: Apply the negative exponent rule, which states that ((a)/(b))^-n = ((b)/(a))^n. ((x^3)/(2^2))^-2 = ((2^2)/(x^3))^2 Step 2: Apply the power of a quotient rule, which states that ((a)/(b))^n = (a^n)/(b^n). ((2^2)/(x^3))^2 = ((2^2)^2)/((x^3)^2) Step 3: Apply the power of a power rule, which states that (a^m)^n = a^mn. ((2^2)^2)/((x^3)^2) = 2^2 × 2x^3 × 2 = (2^4)/(x^6) Step 4: Calculate the numerical value 2^4. 2^4 = 2 × 2 × 2 × 2 = 16 Step 5: Substitute the numerical value back into the expression. (16)/(x^6) Answer: (16)/(x^6) 3. Simplify the powers: x^6y^2z^-3x^-1z^-5 Working out: Step 1: Apply the division rule for exponents ((a^m)/(a^n) = a^m-n) for each variable. For x: (x^6)/(x^-1) = x^6 - (-1) = x^6+1 = x^7 For y: The y^2 term is only in the numerator, so it remains as y^2. For z: z^-3z^-5 = z^-3 - (-5) = z^-3+5 = z^2 Step 2: Combine the simplified terms. x^7y^2z^2 Answer: x^7y^2z^2 Last free one today — make it count tomorrow, or type /upgrade for unlimited.