Evaluate numerical expressions involving exponents (Order of Operations)

Learning Objectives Identify the base and exponent in an exponential expression. Calculate the value of a number raised to a positive integer exponent. Recall and apply the correct Order of Operations (PEMDAS/GEMDAS) to numerical expressions. Accurately evaluate numerical expressions that include exponents and multiple arithmetic operations. Break down complex expressions into smaller, manageable steps for evaluation. Recognize and avoid common errors when evaluating expressions involving exponents. Ever wonder how calculators know what to do first when you type in a long math problem? 🤔 It's all thanks to a special set of rules! In this lesson, you'll learn how to evaluate numerical expressions that include exponents, following a specific set of rules called the...

TermDefinitionExample Numerical ExpressionA mathematical phrase that contains numbers and operation symbols (like +, -, ×, ÷) but no equality sign.Example: $5 + 3 imes 2$ ExponentA small number written above and to the right of a base number, indicating how many times the base should be multiplied by itself.In $2^3$, the '3' is the exponent. BaseThe number that is multiplied by itself according to the exponent.In $2^3$, the '2' is the base. PowerThe entire expression consisting of a base and an exponent, representing the result of multiplying the base by itself a certain number of times.$2^3$ is read as '2 to the power of 3' or '2 cubed'. Order of OperationsA set of rules that dictates the sequence in which mathematical operations should be perform...

Order of Operations (PEMDAS/GEMDAS) 1. **P**arentheses (or **G**rouping Symbols like brackets, braces) 2. **E**xponents 3. **M**ultiplication and **D**ivision (from left to right) 4. **A**ddition and **S**ubtraction (from left to right) This rule ensures that everyone arrives at the same answer when evaluating a numerical expression. Operations within parentheses are always performed first, followed by exponents. Multiplication and division have equal priority and are done from left to right. Similarly, addition and subtraction have equal priority and are done from left to right. Exponent Rule $a^n = a \times a \times \dots \times a$ (n times) This rule defines what an exponent means. The base 'a' is multiplied by itself 'n' times. For example, $4^3 = 4 \...