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 to the simplification problems. d) Simplify M^0 Step 1: Apply the zero exponent rule. Any non-zero number raised to the power of zero is equal to 1. Step 2: Apply the rule to the expression. M^0 = 1 (assuming M ≠ 0) The simplified expression is 1. The statement "M^0 > 1" is incorrect, as M^0 is equal to 1. e) Simplify (2^5 × 2^3)/(sqrt((1+2))) Step 1: Simplify the numerator using the product rule for exponents (a^m × a^n = a^m+n). 2^5 × 2^3 = 2^5+3 = 2^8 Step 2: Calculate the value of 2^8. 2^8 = 256 Step 3: Simplify the denominator. sqrt((1+2)) = sqrt(3) Step 4: Combine the simplified numerator and denominator. (256)/(sqrt(3)) Step 5: Rationalize the denominator by multiplying the numerator and denominator by sqrt(3). (256)/(sqrt(3)) × sqrt(3)sqrt(3) = 256sqrt(3)3 The simplified expression is 256sqrt(3)3. g) Simplify (8-3)^3 Step 1: Perform the subtraction inside the parentheses. 8-3 = 5 Step 2: Raise the result to the power of 3. 5^3 = 5 × 5 × 5 Step 3: Calculate the product. 5 × 5 × 5 = 25 × 5 = 125 The simplified expression is 125. The statement "> 125" is incorrect, as the result is exactly 125. 3 done, 2 left today. You're making progress.