In Exercises 59–70, evaluate each exponential expression. (-1)^33

Verified step by step guidance

1. Identify the base and the exponent in the expression $(-1{)}^{33}$. Here, the base is $-1$ and the exponent is $33$.
2. Recognize that the exponent $33$ is an odd number.
3. Recall the property of exponents: when a negative number is raised to an odd power, the result is negative.
4. Apply this property to the expression $(-1{)}^{33}$. Since $33$ is odd, the result will be $-1$.
5. Conclude that the expression evaluates to $-1$ because raising $-1$ to any odd power results in $-1$.

Key Concepts

Exponential Expressions

Exponential expressions involve a base raised to a power, where the base is multiplied by itself as many times as indicated by the exponent. For example, in the expression a^n, 'a' is the base and 'n' is the exponent. Understanding how to evaluate these expressions is crucial, especially when dealing with negative bases and odd or even exponents.

Properties of Exponents

The properties of exponents provide rules for simplifying and evaluating expressions involving powers. Key properties include the product of powers, power of a power, and the power of a product. Specifically, when the exponent is odd, a negative base raised to that exponent will yield a negative result, while an even exponent would yield a positive result.

Negative Bases

When evaluating expressions with negative bases, the sign of the result depends on whether the exponent is odd or even. A negative base raised to an odd exponent results in a negative value, while raising it to an even exponent results in a positive value. This distinction is essential for correctly evaluating expressions like (-1)^33.