(2^(-1)+3^(-1)+4^(-1))times(3)/(4)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (2^(-1) + 3^(-1) + 4^(-1)) * (3/4)

This expression involves negative exponents and fractions, so let's break it down step-by-step to simplify it:

Understanding Negative Exponents

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

• 2^(-1) = 1/2^1 = 1/2
• 3^(-1) = 1/3^1 = 1/3
• 4^(-1) = 1/4^1 = 1/4

Solving the Expression

1. Calculate the values of the negative exponents: (2^(-1) + 3^(-1) + 4^(-1)) = (1/2 + 1/3 + 1/4)

2. Find a common denominator for the fractions: (1/2 + 1/3 + 1/4) = (6/12 + 4/12 + 3/12)

3. Add the fractions: (6/12 + 4/12 + 3/12) = 13/12

4. Multiply the result by 3/4: (13/12) * (3/4) = 39/48

5. Simplify the fraction: 39/48 = 13/16

Therefore, the simplified value of the expression (2^(-1) + 3^(-1) + 4^(-1)) * (3/4) is 13/16.