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: \((-3) \times (-3) \times (-3) \times (-3) \times (-3)\).
3. Recall the rule for powers of negative numbers: if the exponent is odd, the result is negative; if even, the result is positive.
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 determine 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. The sign of the result depends on whether the exponent is even or odd: an odd exponent yields a negative result, while an even exponent yields a positive result.

Order of Operations

When evaluating expressions, it is important to follow the order of operations (PEMDAS/BODMAS). Parentheses indicate that the operation inside should be performed first, ensuring that the negative sign is included in the base before exponentiation.

Properties of Exponents

Exponents represent repeated multiplication of the base. Understanding that (-3)^5 means (-3) multiplied by itself five times helps in correctly calculating the value and determining the sign of the result.