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
Step 1: Express the bases as powers of prime numbers. We have 27 = 3^3 and 32 = 2^5. Step 2: Substitute these into the expression. ((3^3)^2)/(3) ÷ 2^4(2^5)^-(3)/(5) Step 3: Apply the power rule (a^m)^n = a^mn to simplify the terms. For the numerator: (3^3)^(2)/(3) = 3^3 × (2)/(3) = 3^2 For the denominator: (2^5)^-(3)/(5) = 2^5 × (-(3)/(5)) = 2^-3 Step 4: Rewrite the expression with the simplified terms. (3^2 ÷ 2^4)/(2^-3) Step 5: Calculate the values of the powers. 3^2 = 9 2^4 = 16 2^-3 = (1)/(2^3) = (1)/(8) Step 6: Substitute these values back into the expression. (9 ÷ 16)/(1)8 (9)/(16)(1)/(8) Step 7: Perform the division of fractions. To divide by a fraction, multiply by its reciprocal. (9)/(16) × (8)/(1) (9 × 8)/(16 × 1) (72)/(16) Step 8: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 8. (72 ÷ 8)/(16 ÷ 8) = (9)/(2) The simplified expression is: (9)/(2) That's 2 down. 3 left today — send the next one.