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

Jasonbradley

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Jun 16, 2024

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

This expression involves negative exponents and fractions. Let's break it down step-by-step to simplify it:

Understanding Negative Exponents

Remember that a negative exponent means taking the reciprocal of the base raised to the positive version of the exponent. For example:

• x⁻¹ = 1/x
• y⁻² = 1/y²

Applying the Rules to the Expression

Let's apply this to our expression:

1. (4)^(-1) = 1/4
2. (5)^(-1) = 1/5
3. (5/8)^(-1) = 8/5 (Reciprocal of the fraction)

Now our expression becomes:

(1/4) - (1/5)² * (8/5)

Simplifying Further

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

Now we need to perform the multiplication:

3. (1/4) - (8/125)

Finding a Common Denominator

To subtract fractions, they must have a common denominator. The least common multiple of 4 and 125 is 500.

1. (125/500) - (32/500)

Final Calculation

Now we can subtract:

(125 - 32) / 500 = 93/500

Therefore, the simplified form of the expression (ii) (4)^(-1)-(5)^(-1) ^(2)times((5)/(8))^(-1) is 93/500.