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(81/16)-3/4 X(25/4)-3/2 Divided By 5/2^-3

2 min read Jun 16, 2024
(81/16)-3/4 X(25/4)-3/2 Divided By 5/2^-3

Solving the Expression: (81/16) - 3/4 x (25/4) - 3/2 divided by 5/2^-3

This problem involves several arithmetic operations, so we need to follow the order of operations (PEMDAS/BODMAS) to solve it correctly. Let's break it down step-by-step:

1. Simplify the exponents:

  • 2^-3 = 1/(2^3) = 1/8

2. Rewrite the division as multiplication:

  • Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, dividing by 5/2^-3 is the same as multiplying by (2^-3)/5.

3. Apply the order of operations:

  • Multiplication and Division (from left to right):
    • 3/4 x (25/4) = 75/16
    • (2^-3)/5 = 1/40
  • Addition and Subtraction (from left to right):
    • (81/16) - 75/16 = 6/16 = 3/8
    • 3/8 - 3/2 = -9/8

4. Perform the final multiplication:

  • (-9/8) x (1/40) = -9/320

Therefore, the solution to the expression (81/16) - 3/4 x (25/4) - 3/2 divided by 5/2^-3 is -9/320.

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