Evaluate each expression. See Example 4. (-3)⁵

Verified step by step guidance

1. Recognize that the expression \((-3)^5\) means raising the number \(-3\) to the power of 5, which involves multiplying \(-3\) by itself 5 times.
2. Write the expression as a product: \((-3)^5 = (-3) \times (-3) \times (-3) \times (-3) \times (-3)\).
3. Recall the rule for powers of negative numbers: if the exponent is odd, the result will be negative; if even, the result will be positive.
4. Calculate the absolute value by multiplying 3 by itself 5 times: \(3^5 = 3 \times 3 \times 3 \times 3 \times 3\).
5. Apply the sign determined in step 3 to the result from step 4 to get the final value of \((-3)^5\).

Key Concepts

Exponentiation of Negative Numbers

Raising a negative number to a power involves multiplying the number by itself repeatedly. If the exponent is odd, the result remains negative; if even, the result is positive. For example, (-3)⁵ means multiplying -3 by itself five times.

Order of Operations and Parentheses

Parentheses indicate that the operation inside should be performed first. In (-3)⁵, the negative sign is part of the base, so the entire number -3 is raised to the fifth power, not just 3.

Evaluating Powers

To evaluate a power like (-3)⁵, multiply the base by itself as many times as the exponent indicates: (-3) × (-3) × (-3) × (-3) × (-3). This step-by-step multiplication helps find the exact value.