In Exercises 81–100, evaluate or simplify each expression without using a calculator. In (1/e^6)

Key Concepts

Exponential Functions

Exponential functions are mathematical expressions in the form of f(x) = a * b^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent. In this context, e is a special mathematical constant approximately equal to 2.71828, which is the base of natural logarithms. Understanding how to manipulate exponential expressions is crucial for simplifying or evaluating them.

Reciprocal of Exponents

The reciprocal of an exponential expression, such as 1/e^6, can be rewritten using the property of exponents that states a^(-n) = 1/a^n. This means that 1/e^6 can be expressed as e^(-6). Recognizing this property allows for easier simplification and evaluation of expressions involving exponents.

Simplifying Expressions

Simplifying expressions involves reducing them to their most basic form while maintaining their value. This can include combining like terms, applying exponent rules, and rewriting expressions in a more manageable format. In the case of 1/e^6, applying the reciprocal property leads to a simpler expression, e^(-6), which is easier to interpret and work with.