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(4)^(-1)-(5)^(-1) ^(2)times((5)/(8))^(-1)

2 min read Jun 16, 2024
(4)^(-1)-(5)^(-1) ^(2)times((5)/(8))^(-1)

Simplifying the Expression: (4)^(-1)-(5)^(-1) ^(2) times((5)/(8))^(-1)

This problem involves negative exponents, which can be a bit tricky at first glance. Let's break down the steps to solve this expression:

Understanding Negative Exponents

Remember that a negative exponent indicates the reciprocal of the base raised to the positive value of the exponent. For example:

  • x⁻¹ = 1/x
  • y⁻² = 1/y²

Applying the Rules to the Expression

Let's apply this understanding to our given expression:

  1. (4)^(-1) = 1/4
  2. (5)^(-1) = 1/5
  3. (5)^(-1) ^ (2) = (1/5)² = 1/25
  4. ((5)/(8))^(-1) = (8/5)

Putting It All Together

Now we have: 1/4 - (1/25) * (8/5)

To simplify further, we need to perform the multiplication:

  • (1/25) * (8/5) = 8/125

Finally, we have: 1/4 - 8/125

To subtract these fractions, we need a common denominator:

  • 1/4 = 31.25/125
  • 31.25/125 - 8/125 = 23.25/125

Answer

Therefore, the simplified value of the expression (4)^(-1)-(5)^(-1) ^(2) times((5)/(8))^(-1) is 23.25/125.

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