Rational exponents allow radicals to be written as fractional exponents. To write a radical with an index of n as a rational exponent, the index becomes the denominator and the exponent of the radicand becomes the numerator. The rules of exponents still apply to rational exponents. Expressions with rational exponents are simplified by having no negative exponents, no fractional exponents in the denominator, not being a complex fraction, and having the least possible index for any remaining radicals. Examples show how to evaluate, simplify, and perform operations on expressions with rational exponents.
This will help you in factoring sum and difference of two cubes.
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This powerpoint presentation discusses or talks about the topic or lesson Functions. It also discusses and explains the rules, steps and examples of Quadratic Functions.
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This will help you in factoring sum and difference of two cubes.
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https://tinyurl.com/ybo27k2u
This powerpoint presentation discusses or talks about the topic or lesson Functions. It also discusses and explains the rules, steps and examples of Quadratic Functions.
If you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
https://tinyurl.com/y9muob6q
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I have added to the original presentation in response to one of the comments.... the result of 'x' is correct on slide 7, take a look at the new version of this ppt to clear up any confusion about why...
3. Simplifying Expressions with Rational Exponents
Radicals can also be expressed as a rational (or fractional)
power of an expression. It will sometimes be easier to
use this new method of expressing a radical to simplify a
radical expression.
1
b = b
n n
When you see a radical
expression,
you can convert it to a
fractional power.
4. Example 1 Write each expression in Radical Form
1
6
1) x 6
x
2
3 2
2) m 3
m
5. Example 2 Write each radical using Rational Exponents
1
5
1) b b 5
1 5 7
5 7
2) 3
6x y 6 x y
3 3 3
6. Example 3 Evaluate Each Expression
−1 1
1) 49 2
7
15. Expression with Rational Exponents
An expression with Rational Exponents is simplified when:
1. It has no negative exponents
2. It has no Fractional Exponents in the denominator
3. It is not a Complex Fraction
4. The index of any remaining radical is the least
number possible.
16. Simplifying radicals is often Simplify:
easier using rational exponents. 3
Look at this "rational" example,
3
solved two ways. ==>
3
Solved by Rationalizing the Solved by Using
Denominator Rational Exponents
17. Example 7 Simplify
(8x y ) 3
4 2
−1
3
3 1
1
x 4 y 3
1 2 =
2x 4 y 3 2 xy