- Powers of negative bases
-5^2 = -25, -(5)^2 = 25
- Powers of fractions
(a/b)^3 = a^3/b^3
(sqt2/4)^3 = 2*sqt(2)/64 = sqt2/32
- Negative exponents
a^-b = 1/a^b and 1/a^-b = a^b
- Fractional exponents
x^4/3 = (3sqt(x^4))
- Rationalizing denominators
rules
sqt(a/b) = sqta/sqtb
sqt(ab) = sqta * sqtb
sqta * sqta = a
example
1/sqt2
1/sqt2 * sqt2/sqt2
1sqt2/2
sqt2/2
- Conjugate method
If your denominator is an irrational polynomial, you can multiply the fraction by it's conjugate.
3/(5 - sqt3) = (3/(5-sqt3)) * ((5+sqt3)/(5+sqt3))
Distribute, and then simplify
You can also rationalize out the numerator with this method!
sqt(3x+10) - 2 / x + 2
multiply numerator and denominator by sqt(3x+10) + 2