Advanced exponents

Learning Objectives Identify the base and exponent in an exponential expression. Convert between exponential form and expanded form. Evaluate exponential expressions with positive integer bases and exponents. Compare the values of different exponential expressions. Apply the order of operations when evaluating expressions involving exponents. Solve simple real-world problems involving exponents. Have you ever wondered how scientists describe really big numbers, like the number of bacteria in a colony, or how much data your phone can store? 🤯 Exponents are a super powerful way to write and work with these numbers! In this lesson, we'll dive deeper into exponents, learning how to understand, write, and calculate them. You'll discover how exponents make math easier...

TermDefinitionExample BaseThe base is the number that is multiplied by itself in an exponential expression.In $5^3$, the base is 5. Exponent (or Power)The exponent tells us how many times the base is used as a factor in a multiplication.In $5^3$, the exponent is 3, meaning 5 is multiplied by itself 3 times ($5 \times 5 \times 5$). Exponential FormA way of writing repeated multiplication using a base and an exponent.Instead of $2 \times 2 \times 2 \times 2$, we write $2^4$. Expanded FormWriting an exponential expression as a repeated multiplication of its base.The expanded form of $3^5$ is $3 \times 3 \times 3 \times 3 \times 3$. Value of an Exponential ExpressionThe final result or product obtained after evaluating an exponential expression.The value of $2^3$ is 8, because $2 \times 2 \ti...

Definition of an Exponent $a^n = a \times a \times \dots \times a \text{ (n times)}$ To evaluate an exponential expression, multiply the base by itself the number of times indicated by the exponent. The exponent 'n' must be a positive integer. Exponent of One $a^1 = a$ Any number raised to the power of 1 is simply the number itself. The base is multiplied by itself only one time. Order of Operations (PEMDAS/BODMAS) Parentheses/Brackets, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right) When an expression contains multiple operations, including exponents, always evaluate the exponents before multiplication, division, addition, or subtraction, but after any operations inside parentheses.