(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

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

i dont understand

step-by-step explanation: