Evaluate each expression. -4 * 5³

Verified step by step guidance

1. Identify the expression to evaluate: $-4\times 5^3$.
2. Understand that the expression involves a multiplication of $-4$ and $5^3$.
3. Calculate the exponent first: $5^3$ means multiplying 5 by itself three times, which is $5\times 5\times 5$.
4. Once you have the result of $5^3$, multiply it by $-4$.
5. Remember that multiplying a negative number by a positive number results in a negative number.

Key Concepts

Exponents

Exponents represent repeated multiplication of a number by itself. For example, in the expression 5³, the base 5 is multiplied by itself three times: 5 * 5 * 5, which equals 125. Understanding how to calculate exponents is crucial for evaluating expressions that involve powers.

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. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In the expression -4 * 5³, the exponent is calculated before the multiplication.

Multiplication of Negative Numbers

When multiplying a negative number by a positive number, the result is always negative. In the expression -4 * 125 (where 125 is the result of 5³), the product will be -500. Understanding how to handle negative numbers in multiplication is essential for accurately evaluating expressions.