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 equivalent expressions:
5 × 5 × 5 × 5 × 5
2 × 2 × 2 × 2
2. What is the difference between 3g and g3?
The base number can be written in decimal or fraction form.
1. Fill in the missing expressions for each row. For whole number and decimal bases, use a calculator to find the standard form of the number. For fraction bases, leave your answer as a fraction.
2. Write “five cubed” in all three forms: exponential form, written as a series of products, standard form.
3. Write “fourteen and seven tenths squared” in all three forms.
4. One student thought two to the third power was equal to six. What mistake do you think they made and how would you help them fix their mistake?
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.
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