Rational Exponents WS 4 – Hints
1) cube root of -27 = -? … rewrite with rational exponents … simplify
2) 32 = 2 to what power? … rewrite with rational exponents … simplify
3) rationalize … multiply top & bottom by root 2 … try it to see why 
4) rationalize … multiply top & bottom by cube root of m
5) rationalize … multiply top & bottom by conjugate (root 5 + 1)
6) multiply insides … rewrite with rational exponents … simplify
7) 4th root of 16 = ?... cube it
8) rationalize … multiply top & bottom by 4th root of 9m
9) simplify radicals to get like radicals … combine like terms
10) FOIL … simplify
11) rationalize … multiply top & bottom by conjugate (root 3 – root 6)
12) rationalize … multiply top & bottom by cube root of 3 squared
13) reciprocal … cube root of 27 … square it
14) rewrite with rational exponents … add exponents … simplify
15) rewrite denominator as a radical … rationalize … multiply top & bottom by cube root of 3 … simplify
16) think about powers … 81 = 3 to what power? … rational exponents … simplify
17) multiply exponents … simplify
18) fix negative exponent … add/subtract exponents … simplify
19) reciprocal (the 8 is still neagative!) … cube root … square it
20) multiply exponents … simplify
21) add exponents inside … multiply exponents … simplify
22) multiply all exponents … simplify … fun one 
23) subtract exponents inside … multiply exponents … simplify
24) rewrite as (3/12) to the ½ power … simplify … multiply exponents
25) start with square root of 4 … to the 1/3 power … to the ¼ power … multiply exponents
26) divide 108 by 27 … take the square root … answer to that is inside the other square root
27) subtract exponents … don’t worry about rationalizing here … yuck!
28) more algebraic version of #9
29) simplify inner rad … combine fractions inside … rationalize … multiply top & bottom by cube root of y squared
30) get a common denominator for a common root index … simplify