Videos and solutions to help Grade 6 students learn what are exponents and how to use exponents.
New York State Common Core Math Grade 6, Module 4, Lesson 5
Lesson 5 Student Outcomes
Students discover that 3x = x + x + x is not the same thing as x3 which is x • x • x.
Students understand that a base number can be represented with a positive whole number, positive fraction, or positive decimal and that for any number b, we define bm to be m factors of b where b is the base and m is called the exponent or power of b.
As you evaluate these expressions, pay attention to how you arrive at your answers.
4 + 4 + 4 + 4 + 4 + 4 + 4 +4 + 4 + 4
9 + 9 + 9 + 9 + 9
10 + 10 + 10 + 10 + 10
Multiplication is a faster way to add numbers when the addends are the same.
When we add five groups of 10, we use an abbreviation and a different notation, called multiplication.
10 + 10 + 10 + 10 + 10 = 10 × 5 = 50.
If multiplication is a more efficient way to represent addition problems involving the repeated addition of the same addend, do you think there might be a more efficient way to represent the repeated multiplication of the same factor, as in 10 x 10 x 10 x 10 x 10.
When we add 5 groups of 10, we write 5 × 10, but when we multiply 5 copies of 10, we write 105. So, multiplication by 5 in the context of addition corresponds exactly to the exponent in the context of multiplication.
The repeated factor is called the base and the exponent is also called the power.
There is a special name for numbers raised to the second power. When a number is raised to the second power, it is called squared.
There is also a special name for numbers raised to the third power. When a number is raised to the third power, it is called cubed.
Write each expression in exponential form.
What is the difference between 3g and g3?
The base number can be written in decimal or fraction form.
Exponential Notation for Whole Number Exponents: Let be a non-zero whole number. For any number b, the expression bm is the product of m factors of b.
The number b is called the base, and m is called the exponent or power of b. When m is 1, “the product of one factor of ” just means b, i.e. b1 = b. Raising any non-zero number to the power of 0 is defined to be 1, i.e., b0 = 1 for all b ≠ 0.
Lesson 5 Examples and Exercises
Examples 1 - 5
Go back to Examples 1ִ and use a calculator to evaluate the expressions.
2.1 × 2.1
0.75 × 0.75 × 0.75
The base number can also be a fraction. Convert the decimals to fractions in Examples 7 and 8 and evaluate. Leave your answer as a fraction.
1/2 × 1/2 × 1/2
Exercises 1 - 4
Lesson 5 Exit Ticket
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