10.2 Rational Exponents

Question 1

Define a^1/n

Answer 1

If n is a postive integer greater than 1 and n√a is a real number then a^1/n = n√a [the nth root of a]

Question 2

Define a^m/n

Answer 2

If m and n are positive integers greater than 1 with m/n in simplest form, then a^m/n = (n√a)^ m [ the nth root of a, NOT N TIMES √A)

Question 3

Define a ^-m/n

Answer 3

a^-m/n = 1/a^m/n

Question 4

Product rule for exponents

Answer 4

a^m * a^n = a^m+n

Question 5

Power rule for exponents

Answer 5

(a^m)^n = a^m*n

Question 6

Power rule for products and quotients

Answer 6

(ab)^n = a^n*b^n
(a/c)^n = a^n/c^n

Question 7

Quotient rule for exponents

Answer 7

a^m/a^n=a^m-n

Question 8

Zero exponent

Answer 8

a^0 =1

Question 9

Negative exponent

Answer 9

a^-n=1/a^n