Exponents

1
Exponents

• Mary Guerrant
• 5th hour Trigonometry
• 9/25/06

2
Introduction to Exponents

• Exponents are a shorthand way to show how many
  times a number, called the base, is multiplied
  times itself. A number with an exponent is said
  to be "raised to the power" of that exponent.
• A base of five raised to the second power is
  called "five squared" and means "five times
  five." Five raised to the third power is called
  "five cubed" and means "five times five times
  five." The base can be any sort of number--a
  whole number, a decimal number, or a fraction can
  all be raised to a power.

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Rules of Exponents

• Here are some simple rules to use with exponents.
• a1 aAny number raised to the power of one
  equals the number itself.
• For any number a, except 0, a0 1Any number
  raised to the power of zero, except zero, equals
  one.

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Multiplying Exponents

• For any numbers a, b, and c, ab x ac abc
• This multiplication rule tells us that we can
  simply add the exponents when multiplying two
  powers with the same base.

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Common Mistakes When Multiplying Exponents

• Mistake! Do not multiply the base and the
  exponent. 26 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.

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Scientific Notation

• A number written in scientific notation is
  written as a product of a number between 1 and 10
  and a power of 10.
• Examples7 x 7 x 7 x 7 ?    742 x 2 x 2 x 2 x
  2 x 2 ?   26110    1 53    5 x 5 x 5
  125
• Write the following numbers in scientific
  notation.565,000    5.65 x 1057,325,000
     7.325 x 10691,247,000,000    9.1247 x 1010

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Dividing Exponents

• The quotient rule tells us that we can divide two
  powers with the same base by subtracting the
  exponents. You can see why this works if you
  study the example shown.

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Negative Exponents

• Any nonzero number raised to a negative power
  equals its reciprocal raised to the opposite
  positive power.

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Power of a Product of Factors

• Use the distributive property and multiply the
  exponent outside of the parenthesis by each base
  inside parenthesis.
• (ab)n anbn

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Power of a Power

• To take a power of a power, multiply the
  exponents.
• (am)n amn

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References

• http//www.math.com/school/subject1/lessons/S1U1L8
  GL.html
• http//www.themathpage.com/alg/exponents.htm
• http//www.purplemath.com/modules/exponent.htm