Exponents with decimal bases

Learning Objectives Define and identify the base and exponent in expressions with decimal bases. Rewrite exponential expressions with decimal bases as repeated multiplication. Accurately multiply decimal numbers. Evaluate exponential expressions with positive decimal bases and whole number exponents. Apply the rules of exponents to solve problems involving decimal bases. Recognize and avoid common errors when working with exponents and decimal bases. Have you ever wondered how quickly a small amount can grow, like the interest on savings or the spread of a rumor? 📈 Exponents help us understand this rapid growth! In this lesson, you'll learn how to work with exponents when the base is a decimal number. This builds on your knowledge of exponents and decimal multiplicati...

TermDefinitionExample BaseIn an exponential expression, the base is the number that is being multiplied by itself.In the expression (0.7)³, 0.7 is the base. ExponentThe exponent (or power) is a small number written above and to the right of the base, indicating how many times the base is to be multiplied by itself.In the expression (0.7)³, 3 is the exponent. Exponential ExpressionAn expression that represents repeated multiplication of the same factor, written with a base and an exponent.(0.7)³ is an exponential expression. DecimalA number that contains a decimal point, representing a fraction where the denominator is a power of ten.0.5, 1.25, 0.003 are all decimals. Repeated MultiplicationThe process of multiplying a number by itself multiple times, as indicated by an exponent.0.5² means...

Definition of Exponentiation $$a^n = a \times a \times \dots \times a \quad (n \text{ times})$$ This rule defines what an exponent means: the base 'a' is multiplied by itself 'n' times. This applies whether 'a' is a whole number, a fraction, or a decimal. Multiplying Decimals 1. Multiply the numbers as if they were whole numbers. 2. Count the total number of decimal places in the original numbers. 3. Place the decimal point in the product so it has the same total number of decimal places. This rule is crucial for evaluating exponential expressions with decimal bases. It ensures the correct placement of the decimal point in the final answer.