Exponents and Powers

Introduction

Exponents and powers are fundamental concepts in mathematics that are related to operations involving repeated multiplication.

An exponent refers to the number of times a number, known as the base, is multiplied by itself. The power is the result of this operation. For example, in 2³, 2 is the base, 3 is the exponent, and the power is 8 since 2×2×2=8

Exponents and Powers

• Notation: Exponentiation is denoted by a superscript number after the base: bⁿ, where b is the base and n is the exponent.

• Properties: Exponentiation has several important properties, such as
  • The product of powers property bᵐ × bⁿ = bᵐ⁺ⁿ
  • The power of a power property (bᵐ)ⁿ = bᵐⁿ
  • The power of a product property (ab)ⁿ = aⁿ × bⁿ
  • Negative Exponents: A negative exponent represents the reciprocal of the base raised to the opposite positive exponent: b⁻ⁿ = 1/bⁿ
  • Zero as an Exponent: Any non-zero base raised to the power of zero is equal to one: b⁰ = 1

• Helpful for recognizing notations of base, exponents, power and visualizing graph as student changes the values

Explore Exponential Function Graph

• Graph the exponential function y=aᵇˣ where a is the base and b is the exponent, and both can be adjusted using sliders. The graph is dynamically updated as the sliders are moved, providing an interactive way to visualize how changes in the base and exponent affect the shape of the exponential curve.

Exponential Function Graph Video

• These video will help us explore exponential functions. We will look at functions of the form f(x) = a(b)ˣ, where a is a positive real number and b > 0 but b is not 1. This video will help you understand how changing the values of a and b affect the shape of the graph.
• Describe how changing the value of ‘b’ changes the graph of the function. Explain how the value of ‘a’ changes the graph of the function.