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Rational exponents and radicals
1.
Rational Exponents In other words, exponents
that are ratios or fractions.
2.
Definition of Rational
Exponents For any nonzero number b and any integers m and n with n > 1, 𝑏 𝑚 𝑛 = 𝑛 𝑏 𝑚 = ( 𝑛 𝑏) 𝑚
3.
NOTE: There are 3
different ways to write a rational exponent… 64 2 3 = 3 642 = ( 3 64)2 To simplify,you may need to write it in another form.
4.
Rewrite from exponential to
radical: 1. 36 3 2 = ( 36)3 = (6)3 = 216 2. 3 59=5 9 3 = 53 = 125 Rewrite from radical to exponential:
5.
Examples with negative powers: 3.
64− 1 2 = ( 1 64 ) 1 2= 1 64 = 1 8 4. (1 8 )− 1 3= 8 1 3 = 3 8 = 2
6.
Example with a
variable: 5. 3 𝑥8 𝑥5 = 𝑥 8 3 𝑥 5 2 = 𝑥 8 3 − 5 2=… 𝑥 8 3 ∙ 2 2 − 5 2 ∙ 3 3 = 𝑥 16 6 − 15 6 =… 𝑥 1 6 𝑜𝑟 6 𝑥