(1/2)^3(2/3)^4/5/6^3
(1/8 )(16/81)(216/125)
(2/81)(216/125)
(2/3)(8/125)
16/375
To simplify the expression (1/2)^3 * (2/3)^4 / 5 / 6^3, let's break it down step by step.
Step 1: Simplify the exponent expressions.
(1/8) * (16/81) / 5 / 216
Step 2: Simplify the division operations.
(1/8) * (16/81) * (1/5) * (1/216)
Step 3: Simplify the multiplications.
(16/8) * (1/81) * (1/5) * (1/216)
Step 4: Simplify the fraction division.
2 * 1 * 1 * 1 / 81 * 5 * 216
Step 5: Perform the remaining multiplications.
2 / (81 * 5 * 216)
Step 6: Calculate the numerator.
2
Step 7: Calculate the denominator.
81 * 5 * 216 = 87480
Step 8: Simplify the fraction.
2/87480
So, the simplified form of (1/2)^3 * (2/3)^4 / 5 / 6^3 is 2/87480.