Transcript Rational Exponent Operations

Rational Exponent Operations
Exponent Rules
Copyright © 2013 Lynda Aguirre
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Properties of Radicals
Splitting Property
Changing Rational Exponents to Radical Form
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Exponent Rule #1
Add the Exponents
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To add or subtract fractions
you need the same
denominators(bottoms)
These are already the same
Copyright © 2013 Lynda Aguirre
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To add or subtract fractions
you need the same
denominators(bottoms)
See lesson:
LCM
Rational
Form
We need to change the second
fraction’s denominator into a 4.
(Multiply 2nd fraction by 2, top and bottom)
Simplify the radical
(see splitting property)
Radical
Form
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Exponent Rule #2
Multiply the Exponents
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To multiply fractions
Multiply straight across
(tops, then bottoms)
𝑡𝑜𝑝 × 𝑡𝑜𝑝
𝑏𝑜𝑡𝑡𝑜𝑚 × 𝑏𝑜𝑡𝑡𝑜𝑚
Reduce the fraction
Rational
Form
Radical
Form
(divide each of them by 2)
Read the instructions to see whether
the answer should be in
Rational Form or Radical Form .
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Exponent Rule #3
Subtract the Exponents
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To subtract fractions
You must have common
denominators
(The same number on the bottom)
Rational
Form
Radical
Form
These bottom numbers
are already the same
Read the instructions to see whether
the answer should be in
Rational Form or Radical Form .
Note: Always check to see if you can reduce the fractions and simplify radicals
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To subtract fractions
You must have common
denominators
(The same number on the bottom)
We need to change both denominators into
a 12.
Rational
Form
(Multiply 1st fraction by 4, and 2nd fraction by 3)
Radical
Form
Note: Always check to see if you can reduce the fractions and simplify radicals
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Exponent Rule #4
OR
Negative Exponents: Move it!
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PARKING TICKET: This term is in
the wrong parking place. Move
it and remove the ticket (the
negative sign)
1) Write as a fraction
Rational
Form
2) Move term to the
bottom.
3) Remove the negative power
Simplify the radical: splitting property
Radical
Form
Copyright © 2013 Lynda Aguirre
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PARKING TICKET: This term is in
the wrong parking place. Move
it and remove the ticket (the
negative sign)
1) Move negative term
to the top.
Rational
Form
2) Remove the negative power
Simplify the radical: splitting property
Radical
Form
Copyright © 2013 Lynda Aguirre
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Practice Problems
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Practice Problems
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Practice Problems
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Practice Problems
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More Exponent Rules with Rational Exponents