Evaluate each expression. (-3)^5

Verified step by step guidance

1. Identify the base and the exponent in the expression $(-3{)}^5$. Here, the base is $-3$ and the exponent is $5$.
2. Understand that the exponent $5$ indicates that the base $-3$ should be multiplied by itself a total of 5 times.
3. Write out the expression as a repeated multiplication: $(-3)\times (-3)\times (-3)\times (-3)\times (-3)$.
4. Calculate the product step by step, starting with the first two numbers: $(-3)\times (-3)=9$.
5. Continue multiplying the result by the next $-3$ until all factors are used: $9\times (-3)$, then $(-27)\times (-3)$, and finally $81\times (-3)$.

Key Concepts

Exponents

Exponents represent the number of times a base is multiplied by itself. In the expression (-3)^5, the base is -3, and the exponent is 5, indicating that -3 should be multiplied by itself five times. Understanding how to handle positive and negative bases with exponents is crucial for evaluating such expressions.

Negative Numbers

Negative numbers are values less than zero, and they can affect the outcome of mathematical operations, especially when raised to an exponent. In this case, raising a negative number to an odd exponent results in a negative product, which is important to remember when evaluating expressions like (-3)^5.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. When evaluating expressions, it is essential to follow these rules, particularly when dealing with exponents, to arrive at the correct answer. In this case, the exponentiation is performed before any other operations.