(81/16)-3/4 X(25/9)-3/2 Divided By 5/2^-3

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (81/16) - 3/4 x (25/9) - 3/2 divided by 5/2^-3

This problem requires us to follow the order of operations (PEMDAS/BODMAS) to arrive at the correct solution. Let's break down the steps:

Step 1: Evaluate the exponent

• 2^-3 = 1/2^3 = 1/8

Step 2: Simplify the division

• 5 / (1/8) = 5 * 8 = 40

Step 3: Perform multiplication

• (3/4) * (25/9) = (3 * 25) / (4 * 9) = 75/36 = 25/12

Step 4: Simplify the expression

• (81/16) - (25/12) - (3/2) / 40
• To perform addition and subtraction, we need a common denominator. The least common multiple of 16, 12, and 40 is 240.
• (81/16) * (15/15) = 1215/240
• (25/12) * (20/20) = 500/240
• (3/2) * (120/120) = 360/240
• Now we have: (1215/240) - (500/240) - (360/240) / 40
• (1215 - 500 - 360) / 240 = 355/240

Step 5: Divide by 40

• (355/240) / 40 = (355/240) * (1/40) = 355/9600

Therefore, the simplified form of the expression (81/16) - 3/4 x (25/9) - 3/2 divided by 5/2^-3 is 355/9600.