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
Hey Jayden, good to see you again. Here are the simplifications: a) Step 1: Apply the negative exponent rule a^-n = (1)/(a^n). x^-3y^-2 = (y^2)/(x^3) The expression is already simplified. (y^2)/(x^3) b) Step 1: Separate the terms and apply the exponent rule (a^m)/(a^n) = a^m-n. (2x^n y^4)/(2x^n-1) y^3 = ((2)/(2)) ((x^n)/(x^n-1)) ((y^4)/(y^3)) Step 2: Simplify each part. 1 · x^n-(n-1) · y^4-3 = x^n-n+1 · y^1 Step 3: Combine the terms. x^1 y^1 = xy xy c) Step 1: Simplify the innermost exponent using ((a)/(b))^-n = ((b)/(a))^n. (((1)/(2))^-2)^-3 = (2^2)^-3 Step 2: Simplify the term inside the parenthesis. (4)^-3 Step 3: Apply the negative exponent rule a^-n = (1)/(a^n). 4^-3 = (1)/(4^3) Step 4: Calculate the final value. (1)/(4 × 4 × 4) = (1)/(64) (1)/(64) d) Step 1: Express the bases 32 and 8 as powers of 2. 32 = 2^5 8 = 2^3 Substitute these into the expression. (2^5)^3a+2(2^3)^a+b Step 2: Apply the exponent rule (a^m)^n = a^m × n. 2^5(3a+2)2^3(a+b) = 2^15a+102^3a+3b Step 3: Apply the exponent rule (a^m)/(a^n) = a^m-n. 2^(15a+10) - (3a+3b) Step 4: Simplify the exponent. 2^15a+10-3a-3b = 2^12a-3b+10 2^12a-3b+10 Send me the next one 📸