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Here are some simple rules to use with exponents.
ALERT! These are mistakes that students often make when dealing with exponents.
Mistake! Do not multiply the base and the exponent. 2^{6} is not equal to 12, it's 64!
Mistake! The multiplication rule only applies to expressions with the same base. Four squared times two cubed is not the same as 8 raised to the power two plus three.
Mistake! The multiplication rule applies just to the product, not to the sum of two numbers.
Scientific
Notation
What happens when you're using a calculator and your answer is too long to
fit in the window? Use a calculator to multiply these 2 numbers:
60,000,000,000,000
x 20,000,000,000
You'll discover a short way of writing very long numbers. This is called scientific
notation, or E notation on a calculator ("E" stands for "Exponent").
A number written in scientific notation is written as a product of a number
between 1 and 10 and a power of 10.
For example, to write 127,680,000 in scientific notation, change the number to a number between 1 and 10 by moving the decimal point 8 places to the left. Then multiply by 10 raised to the power of the number of places you had to move the decimal pointthat is, 108:
127,680,000
= 1.2768 x 10^{8}
On your calculator window, the base of 10 is not shown; the E means "10
raised to the following power."
Examples
7 x 7 x 7 x 7 = ? 7^{4}
2 x 2 x 2 x 2 x 2 x 2 = ? 2^{6}
1^{10} = 1
5^{3} = 5 x 5 x 5 = 125
Write the following
numbers in scientific notation.
565,000
= 5.65 x 10^{5}
7,325,000 = 7.325 x 10^{6}
91,247,000,000 = 9.1247 x 10^{10}
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