Exponents & Radicals

Question 1

(x^m)*(x^n)

Answer 1

x^(m+n)

Question 2

(x^m)/(x^n)

Answer 2

x^(m-n)

Question 3

(x^m)^n

Answer 3

x^(mn)

Question 4

(xy)^m

Answer 4

(x^m)(y^m)

Question 5

(x/y)^m

Answer 5

(x^m)/(y^m)

Question 6

x^(-m)

Answer 6

1/(x^m)

Question 7

If k^(x+y)=w, what is k^x in terms of w

Answer 7

w/(k^y)=k^x

since (k^x)*(k^y)=k^(x+y)

Question 8

If ax-y=c, what is the value of (z^x)/(w^y) , given w^a=z

Answer 8

• figure out how to manipulate one of the equations to look like the other (eg. since (a^m)/(a^n)=a^(m-n), find how many times a, z goes into w (or vice versa) and apply w^ax/w^y=w^(ax-y))*
• the fact w^a=z is never explicitly said on the SAT so be on the lookout for that*
  1. (z^x)/(w^y)=(w^ax)/w^y
  2. w^(ax-y)=w^c

Question 9

Difference between x^(3/2) and (√(x))^3

Answer 9

None… they are the same

Question 10

x^(m/k)

Answer 10

k’th root of x^m

Question 11

Simplify √k

Answer 11

1. Find all the factors of x and write √factors of x
2. take out any pairs
   * essentially, take out any squares*