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(-(1)/(3))^(4)- (-(1)/(3))^(8)times(-(1)/(3))^(5)

2 min read Jun 16, 2024
(-(1)/(3))^(4)- (-(1)/(3))^(8)times(-(1)/(3))^(5)

Simplifying the Expression: (-(1)/(3))^(4)- (-(1)/(3))^(8)times(-(1)/(3))^(5)

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

Understanding Exponents

  • Exponents indicate repeated multiplication. For example, (-(1)/(3))^(4) means (-(1)/(3)) * (-(1)/(3)) * (-(1)/(3)) * (-(1)/(3)).

Applying the Laws of Exponents

  • Multiplication of powers with the same base: When multiplying powers with the same base, we add the exponents. Therefore, (-(1)/(3))^(8) * (-(1)/(3))^(5) = (-(1)/(3))^(8+5) = (-(1)/(3))^(13).

Calculating the Expression

  1. Calculate the individual powers:

    • (-(1)/(3))^(4) = (1/3) * (1/3) * (1/3) * (1/3) = 1/81
    • (-(1)/(3))^(13) = (1/3) * (1/3) * (1/3) ... (13 times) = 1/1594323

  2. Substitute the values back into the original expression:

    • (-(1)/(3))^(4) - (-(1)/(3))^(8) * (-(1)/(3))^(5) = 1/81 - 1/1594323

  3. Simplify the subtraction:

    • 1/81 - 1/1594323 = (1594323 - 81) / (81 * 1594323) = 1594242 / 129140163

Final Result

The simplified form of the expression (-(1)/(3))^(4)- (-(1)/(3))^(8)times(-(1)/(3))^(5) is 1594242 / 129140163.

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