Understanding exponents

Learning Objectives Define and identify the base, exponent, and power in an exponential expression. Write repeated multiplication in exponential form. Expand exponential expressions into repeated multiplication. Evaluate numerical expressions involving whole number exponents. Apply the rules for exponents of zero and one. Solve simple real-world problems involving exponents. Compare the values of different exponential expressions. Have you ever wondered how scientists describe incredibly large numbers, like the number of cells in your body, or how computer memory is measured? 🚀 In this lesson, you'll discover exponents, a powerful mathematical shortcut for repeated multiplication. Understanding exponents will help you work with very large or very small numbers more...

TermDefinitionExample BaseThe number that is being multiplied by itself in an exponential expression.In $5^3$, the base is 5. ExponentThe small number written above and to the right of the base, indicating how many times the base is multiplied by itself.In $5^3$, the exponent is 3. PowerThe entire expression consisting of a base and an exponent, representing repeated multiplication.$5^3$ is read as '5 to the power of 3' or '5 cubed'. Exponential FormA way of writing repeated multiplication using a base and an exponent.$2 imes 2 imes 2 imes 2$ in exponential form is $2^4$. Expanded FormWriting an exponential expression as a product of its base multiplied by itself the number of times indicated by the exponent.$3^5$ in expanded form is $3 imes 3 imes 3 imes 3 imes...

Definition of an Exponent $a^n = a \times a \times \dots \times a$ (n times) This rule defines what an exponent means: 'a' (the base) is multiplied by itself 'n' (the exponent) times. Exponent of One $a^1 = a$ Any non-zero number raised to the power of 1 is simply the number itself. The base is multiplied by itself only once. Exponent of Zero $a^0 = 1$ (for $a \neq 0$) Any non-zero number raised to the power of 0 is always equal to 1. This is a special rule to remember.