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(5/9)-2 X (3/5)-3x (3/5)0

2 min read Jun 16, 2024
(5/9)-2 X (3/5)-3x (3/5)0

Simplifying the Expression: (5/9)-2 x (3/5)-3x (3/5)0

This expression involves fractions, exponents, multiplication, and subtraction. To solve it, we need to follow the order of operations (PEMDAS/BODMAS):

  1. Parentheses/Brackets: None in this case.
  2. Exponents: We have two exponents:
    • (5/9)-2: This means (5/9) multiplied by itself twice.
    • (3/5)0: Any number raised to the power of 0 equals 1.
  3. Multiplication and Division (from left to right):
    • (5/9)-2: Calculate this first. Remember, a negative exponent means taking the reciprocal.
    • -2 x (3/5): Multiply these.
    • -3 x (3/5)0: Since (3/5)0 = 1, this simplifies to -3 x 1.
  4. Addition and Subtraction (from left to right):
    • Add and subtract the results of the previous calculations.

Let's break it down step-by-step:

  1. (5/9)-2 = (9/5)2 = 81/25
  2. -2 x (3/5) = -6/5
  3. -3 x (3/5)0 = -3 x 1 = -3

Now, we have:

81/25 - 6/5 - 3

To subtract these fractions, we need a common denominator:

81/25 - 30/25 - 75/25

Finally, we can combine the numerators:

(81 - 30 - 75)/25 = -24/25

Therefore, the simplified expression is -24/25.

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