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 explanations for the laws of exponents you mentioned: 1. Quotient Rule This rule states that when dividing two powers with the same base, you subtract the exponents. (a^m)/(a^n) = a^m-n Example: (x^7)/(x^3) = x^7-3 = x^4 The quotient rule is: (a^m)/(a^n) = a^m-n 2. Power of a Product Rule This rule states that when a product of bases is raised to an exponent, you apply the exponent to each base in the product. (ab)^n = a^n b^n Example: (2x)^3 = 2^3 x^3 = 8x^3 The power of a product rule is: (ab)^n = a^n b^n 3. Power of a Quotient Rule This rule states that when a quotient (fraction) is raised to an exponent, you apply the exponent to both the numerator and the denominator. ((a)/(b))^n = (a^n)/(b^n) Example: ((y)/(z))^4 = (y^4)/(z^4) The power of a quotient rule is: ((a)/(b))^n = (a^n)/(b^n) That's 2 down. 3 left today — send the next one.