DLIELC Presentation Exponent

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The Laws of Exponents
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Exponents
Exponent / Raising
Power
Base
53 means 3 factors of 5 or 5 x 5 x 5
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The Laws of Exponents
1 Exponential form The exponent of a power
indicates how many times the base multiplies
itself.
n factors of x
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2 Square form The exponent of a power two
times the base multiplies itself.
Ex 92 9x9 83
3 Cube form The exponent of a power three
times the base multiplies itself.
Ex 93 9x9x9 729
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The Invisible Exponent

• When an expression does not have a visible
  exponent its exponent is understood to be 1.

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4 Multiplying Powers If you are multiplying
Powers with the same base, KEEP the BASE ADD
the EXPONENTS!
So, I get it! When you multiply Powers, you add
the exponents!
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5 Dividing Powers When dividing Powers with
the same base, KEEP the BASE SUBTRACT the
EXPONENTS!
So, I get it! When you divide Powers, you
subtract the exponents!
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Try these
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(No Transcript)
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6 Negative Law of Exponents If the base is
powered by the negative exponent, then the base
becomes reciprocal with the positive exponent.
So, when I have a Negative Exponent, I switch
the base to its reciprocal with a Positive
Exponent. Ha Ha! If the base with the negative
exponent is in the denominator, it moves to the
numerator to lose its negative sign!
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Simplifying Radicals
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Radicands

• Radical expression is an expression containing a
  radical sign.
• Radicand is the expression under a radical sign.
• Note that if the radicand of a square root is a
  negative number, the radical is NOT a real number.

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If x2 y then x is a square root of y.
In the expression , is the radical
sign and64 is the radicand.

• Find the square root
• 8

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Radicals - definitions

• The definition of is the number that
  when multiplied by itself 2 times is x (which is
  the factor or root).

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Simplify

This is a piece of cake!

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Converting roots into fractional exponents

• Any radical expression may be transformed into an
  expression with a fractional exponent. The key is
  to remember that the fractional exponent must be
  in the form

For example
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Radical Expression
In general, if n is a multiple of m, then
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The End
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