Question

Question 5: Write each of the following in the form 9^n
(a) 81
(b) 3
(C) 27​

Answer 1

(a) 9^2

(b) 9^0.5

(c) 9^1.5

Explanation:

We need to find n such that 9^n = value indicated.

Recall that n=2 is a square, so

(a) 9^2=9*9=81

Recall that n=0.5 (or 1/2) is a square root, because 9^0.5 * 9^0.5 = 9^1 = 9, so

(b) 9^0.5 = 3, because 3*3 = 9

Recall that multiplication of two powers with the same base is the sum of the exponents, e.g. 9^a * 9^b = 9^(a+b).

Therefore,

(c) 27 = 9*3 = 9^1 * 9^0.5 = 9^(1+0.5) = 9^1.5

Answer 2

a) 9^2

b) 9^(1/2)

c) 9^(3/2)

Explanation:

It is perhaps easier to start by using 3^n.

3 = 3^1

27 = 3^3

81 = 3^4

Recognize that 3 = 9^(1/2) and replace 3 in each of the above. The applicable rule of exponents is (a^b)^c = a^(bc).

a) 81 = (9^(1/2))^4 = 9^2

b) 3 = 9^(1/2)

c) 27 = (9^(1/2))^3 = 9^(3/2)