Evaluate each expression. (-3)⁵

Verified step by step guidance

1. Recognize that the expression is \((-3)^5\), which means \(-3\) is raised to the 5th power.
2. Recall that raising a number to a power means multiplying that number by itself as many times as the exponent indicates. So, \((-3)^5 = (-3) \times (-3) \times (-3) \times (-3) \times (-3)\).
3. Understand that since the base is negative and the exponent is an odd number (5), the result will be negative because multiplying an odd number of negative factors results in a negative product.
4. Calculate the absolute value by multiplying 3 by itself 5 times: \(3 \times 3 \times 3 \times 3 \times 3\).
5. Combine the sign from step 3 with the absolute value from step 4 to get the final value of \((-3)^5\).

Key Concepts

Exponents and Powers

An exponent indicates how many times a base number is multiplied by itself. For example, in (-3)^5, the base is -3 and the exponent 5 means multiplying -3 by itself five times.

Negative Base with Exponents

When raising a negative number to a power, the sign of the result depends on whether the exponent is even or odd. An odd exponent keeps the result negative, while an even exponent makes it positive.

Order of Operations and Parentheses

Parentheses indicate that the negative sign is part of the base. Without parentheses, the exponent applies only to the number, not the negative sign. Here, (-3)^5 means the entire -3 is raised to the fifth power.