Evaluate each expression. -4 ∙ 5³

Verified step by step guidance

1. Identify the expression to evaluate: \(-4 \times 5^{3}\).
2. Recall the order of operations (PEMDAS): exponents are evaluated before multiplication.
3. Calculate the exponent part first: \$5^{3}$ means \(5 \times 5 \times 5\).
4. Multiply the result of the exponent by \(-4\): \(-4 \times (5^{3})\).
5. Write the final expression ready for evaluation: \(-4 \times 125\) (since \$5^{3} = 125$).

Key Concepts

Order of Operations

The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed to ensure consistent results. Typically remembered by PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), it requires evaluating exponents before multiplication.

Exponents

Exponents indicate how many times a base number is multiplied by itself. For example, 5³ means 5 multiplied by itself three times (5 × 5 × 5), which equals 125. Understanding exponents is essential for correctly simplifying expressions involving powers.

Multiplication of Integers

Multiplication of integers involves combining numbers with their signs. Multiplying a negative number by a positive number results in a negative product. In this problem, -4 multiplied by 125 results in -500, demonstrating the rule for multiplying integers with different signs.