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What you will learn from this videoWhat you will learn
- We'll learn about exponents!
- We will also learn how to solve equations that have exponents.
- And we'll see how this knowledge can help us learn about cool organisms, measure earthquakes and even harvest fruit!
- Discussion Questions
Before Video
You have used powers of 10 before. What does 10^{3} mean? What does 10^{5} mean?ANSWER10^{3} = 10 × 10 × 10, 10^{5} = 10 × 10 × 10 × 10 × 10. The little number tells you how many times to multiply the big number. It is not the same as 10 × 3 or 10 × 5.
I use GMS. It’s an acronym to help remember the order of operations. G comes first and that means solve Groupings first, or parts of an expression that are in parentheses. Then M stands for Multiplication and division, which I do as I see them from left to right. Then S stands for Subtraction and addition, which I also work out from left to right.
First is G, so I take care of groupings first. (2 + 1) is in parentheses, so evaluate that first. 2 + 1 = 3, so I can rewrite the expression as 3+6÷2×3-5. Next is M, so take care of the multiplication and division as they occur from left to right. First is 6÷2 = 3, so the expression becomes 3+3×3-5. Next, 3 × 3 = 9, so the expression is now 3+9-5. Since only S, or subtraction and addition, is left, I can work out the rest from left to right. 3+9-5=12-5=7.
[ggfrac]5 x 2 x 4/3 x 2 x 4 x 4[/ggfrac]ANSWEROne of the 2s in the numerator and one of the 2s in the denominator can simplify to 1, and one of the 4s in the numerator and one of the 4s in the denominator can simplify to 1. Then all that’s left is [ggfrac]5 x 1 x 1/3 x 1 x 1 x 4[/ggfrac] = [ggfrac]5/3 x 4[/ggfrac].
No. Multiplication is commutative and associative. Commutative means that I can rearrange a multiplication expression and still get the same answer. Associative means that I can multiply the expression in backward order or scrambled order, and still get the same answer.
After Video
How do you say 2^{5} in words? Which part is called the exponent? Which part is the base?ANSWERI say “2 to the power of 5.” It means that 2 is multiplied 5 times. 2 is the base, which is the number I use to multiply. 5 is the exponent, which tells how many times to multiply.
No. 3 × 4 = 12, but 3^{4} means 3 × 3 × 3 × 3, which is equal to 81. Big difference!
I can always remember exponent rules by recalling what exponents mean and by expanding the expression, which means writing it the long way. 2^{3} means 2 × 2 × 2 and 2^{5} means 2 × 2 × 2 × 2 × 2. Then 2^{3} x 2^{5} means (2 × 2 × 2) × (2 × 2 × 2 × 2 × 2). I count that 2 is multiplied 8 times, so I can write that as 2^{8}. Notice that 3 + 5 = 8, so the rule for multiplying powers with the same base must be that I add together the exponents! I can use my calculator to find out that 2^{8} = 256.
When a power is raised to another power, I multiply the exponents. 2 × 4 = 8, so (2^{2})^{4} = 2^{8} = 256. If I forget the rule, I can expand again!
No. The rule for dividing powers says that if I divide two powers that have the same base, I can subtract their exponents. But 2^{6} and 3^{6} have different bases. That means I can’t use the rule. I can test this answer by expanding and seeing what happens!
- Vocabulary
- Exponent DEFINE
Tells how many times a number is multiplied by itself.
- Power DEFINE
A term that uses an exponent.
- Base DEFINE
The number that gets multiplied by itself.
- Superscript DEFINE
A number that is written smaller, a little above and to the right of another number, like an exponent.
- GEMS DEFINE
An acronym that helps us remember the order of operations.
- Exponent form DEFINE
When a term uses exponents, like 2^{5}.
- Expanded form DEFINE
When we write a power as a multiplication expression.
- Exponent DEFINE
- Reading Material
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- Practice Number Problems
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