Evaluate the expression. Write fractions in simplest form....

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Key Concepts

Even Exponents

When a number is raised to an even exponent, the result is always nonnegative because any negative sign is effectively 'canceled out.' This fact explains why (-3)^6 results in a positive number, as the six multiplications of -3 yield a positive result.

Order of Operations

Understanding the order of operations is essential when evaluating expressions. In expressions involving exponentiation and negation, exponentiation is performed before applying the negative sign unless parentheses indicate otherwise. This distinction is crucial for correctly interpreting expressions like (-3)^6 and -3^6.

Exponentiation with Negative Bases

Exponentiation with negative bases can be tricky because the presence or absence of parentheses changes the result. When the negative sign is within the parentheses as in (-3)^6, the entire negative number is raised to the power, whereas without parentheses as in -3^6, the exponent applies only to 3 and then the negative sign is applied.

Fraction Simplification

Simplifying fractions involves recognizing when the numerator and denominator are opposites or have a common factor. In this context, after evaluating the exponentiation in both the numerator and the denominator, the fraction reduces to a simpler form through cancellation of common factors.

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