Simplify [4]81x-8z4 and [3]256a6b12c9

You're on a roll — I will solve the remaining problems you've marked. 1. Simplify i) [4]81x^-8z^4 Step 1: Apply the property [n]abc = [n]a[n]b[n]c. [4]81 × [4]x^-8 × [4]z^4 Step 2: Evaluate each term. [4]81 = 3 (since 3^4 = 81) [4]x^-8 = x^-8/4 = x^-2 [4]z^4 = z Step 3: Combine the simplified terms. 3 × x^-2 × z = (3z)/(x^2) The simplified expression is (3z)/(x^2). ii) [3]256a^6b^12c^9 Step 1: Factorize the constant term 256 to find its perfect cube factors. 256 = 64 × 4 = 4^3 × 4 Step 2: Apply the property [n]abc = [n]a[n]b[n]c and [n]x^m = x^m/n. [3]64 × 4 × a^6 × b^12 × c^9 [3]64 × [3]4 × [3]a^6 × [3]b^12 × [3]c^9 Step 3: Evaluate each term. [3]64 = 4 (since 4^3 = 64) [3]4 [3]a^6 = a^6/3 = a^2 [3]b^12 = b^12/3 = b^4 [3]c^9 = c^9/3 = c^3 Step 4: Combine the simplified terms. 4 × [3]4 × a^2 × b^4 × c^3 = 4a^2b^4c^3[3]4 The simplified expression is 4a^2b^4c^3[3]4. vii) sqrt(((216)^2)/(3)) × (125)^2(0.04)^-3 Step 1: Simplify each term in the expression. (216)^(2)/(3) = (6^3)^(2)/(3) = 6^3 × (2)/(3) = 6^2 = 36 (125)^2 = (5^3)^2 = 5^6 (0.04)^-3 = ((4)/(100))^-3 = ((1)/(25))^-3 = (25)^3 = (5^2)^3 = 5^6 Step 2: Substitute the simplified terms back into the square root. sqrt((36 × 5^6)/(5^6)) Step 3: Cancel out common terms. sqrt(36) Step 4: Evaluate the square root. sqrt(36) = 6 The simplified expression is 6. Got more? Send 'em 📸