5) Radicals and Rational Exponents

cancel out root if you can by multiplying exponent by that number

important summary

Fraction raised to negative exponent

means the reciprocal of that if it was positive also fraction to exponent (also means expo applies to both numerator and denom)

important

same base of exponent (in this case h) = can add 13^2 =

to add or subtract roots

same exact root (inside and outside) --- can add coeff (stay single)

keep in mind next steps after 8+8 plus root 8

simplify whats in the radical to two radicals

tricky

a+b root ... when solving the equaiton ignore. the numbers that are similar to positions of given ^^ remember that there is still a 1 in front of root

negative --- positive exponent (reciprocal)

a^-2 1/a^2

fraction raised to the fraction

applies to both numerator and denom (cancel sign if both negative)

weakness: factoring and common denominator

factor quadratic - if it is a quadratic multiply each one by what it needs to be multiplied with if you want to make it the same denom (when multiplying its always = 1) --- top and bottom the same for everything --- just factor --- if insecure about it not being a perfect quadratic bc missing an ex ^^ so that something in fraction will cancel out

^^ again - find the largest perfect square that can divide the number

then multiply that (under a root) with what it needs to be multiplied with (under a root) working backwards --- answer choices (square the one not in root and times by the one in root