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 for the expressions: 1. Simplify the expression (30x^6)/(3x^-2) Step 1: Divide the numerical coefficients. (30)/(3) = 10 Step 2: Apply the exponent rule (a^m)/(a^n) = a^m-n for the x terms. x^6 · x^-(-2) = x^6 - (-2) = x^6+2 = x^8 Step 3: Combine the simplified numerical and variable parts. 10x^8 The simplified expression is: 10x^8 2. Simplify ((x^3)/(2^2))^-2 Step 1: Apply the exponent rule ((a)/(b))^n = (a^n)/(b^n) and (a^m)^n = a^mn. (x^3)^-2(2^2)^-2 Step 2: Simplify the exponents in the numerator and denominator. x^3 × (-2)2^2 × (-2) = x^-62^-4 Step 3: Apply the negative exponent rule a^-n = (1)/(a^n) to move terms with negative exponents to the opposite part of the fraction. (2^4)/(x^6) Step 4: Calculate the value of 2^4. 2^4 = 2 × 2 × 2 × 2 = 16 Step 5: Substitute the value back into the expression. (16)/(x^6) The simplified expression is: (16)/(x^6) That's 2 down. 3 left today — send the next one.