(a) Express each of these numbers as a product of its prime factors in index
notation.
(i) 12
(ii) 144
(iii) 5040

(i) 12 = 2 x 2 x 3 => 2² x 3¹

(ii) 144 = 2 x 2 x 2 x 2 x 3 x 3 => 2⁴ x 3²

(iii) 5040 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 => 2⁴ x 3² x 5¹ x 7¹

Step-by-step explanation:

(a) Express each of these numbers as a

product of its prime factors in index

notation.

(i) 12 = 2 x 2 x 3 => 2² x 3¹

(ii) 144 = 2 x 2 x 2 x 2 x 3 x 3 => 2⁴ x 3²

(iii) 5040 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 => 2⁴ x 3² x 5¹ x 7¹

This question is incomplete, here is the complete question:

Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current revenues, they receive an additional $50,000,000 grant. This would allow them to reduce average tuition by how much?

A) $1388.89

B) $3571.43

C) $5555.56

D) $9500.00

E) $25888.89

number of students = 36,000

A) $

1388.89

Step-by-step explanation:

the college received additional grant which is $50,000,000

and the number of students is 36,000,

and we also know that expenses and enrollment remained the same.

So if we have more money (grants) and nothing changed (expenses remain the same)

dividing the grant by the number of students will show just how much the average tuition fee would be reduced

therefore R = G/n

R = 50,000,000 / 36000

R = 1,388.888 ≈  $1388.89