Introduction to Powers Notes PDF

# MATH 9 ## 1.1 Introduction to Powers ### Notes **Power:** a simple way to express repeated multiplication $4 \times 4 \times 4 \times 4 \times 4 \times 4$ is the same as $4^6$ and is read 'four to the exponent of six'. | | | | | ------------- | ----- | ----------...

# MATH 9 ## 1.1 Introduction to Powers ### Notes **Power:** a simple way to express repeated multiplication $4 \times 4 \times 4 \times 4 \times 4 \times 4$ is the same as $4^6$ and is read 'four to the exponent of six'. | | | | | ------------- | ----- | ---------- | | **Power** | $4^6$ | **Exponent** | | | | **Base** | The entire expression is called a **power**. The **base** in a power is the number being multiplied (the repeated factor) - 4 is the base. The **exponent** tells you how many times to use the base as a factor - 6 is the exponent. ### Example 1 Complete the following. $3^5$ is read as ______________________________. The base is _____ and the exponent is _____. ### Forms of a Number When working with powers there are three different ways to express the number: 1. **Exponential Notation:** the expression is written as a power - using a base and an exponent. - $7^4$ is written in exponential form. 2. **Factored Form:** the power is writing as a multiplication question - $7 \times 7 \times 7 \times 7$ is the factored form of $7^4$ 3. **Standard Form:** is the value of the power...it means to work out the multiplication. - 2401 is the standard form of $7^4$ ### Example 2 Complete the chart. | Exponential Notation | Factored Form | Standard Form | | --------------------- | --------------------------------- | -------------- | | $2^5$ | | | | $8^3$ | | | | | $7 \times 7 \times 7 \times 7$ | | | | $12 \times 12 \times 12$ | | | $3^4$ | | 36 | | | | 1000 | | | $\frac{3}{5} \times \frac{3}{5} \times \frac{3}{5}$ | 125 | | $(\frac{1}{2})^3$ | | | | | $0.2 \times 0.2 \times 0.2 \times 0.2$ | 49 | | | | 16 | | one-quarter cubed = $(\frac{1}{4})^3$ | | 216 |