# Integers

#### dagr8est

##### Junior Member
If x is an integer, which of the following could be x^3?

i) 1.25(10^17)
ii) 12.5(10^-12)
iii) 0.125(10^-12)

This is what I did.

i) 1.25(10^17) = 125(10^15) = [5(10^5)]^3, then x = 500000

ii) 12.5(10^-12) = 125(10^-13) = [5(10^-13/3)]^3, then x = 0.00023207...

iii) 0.125(10^-12) = 125(10^-15) = [5(10^-5)]^3, then x = 0.00005

I answered only i since 0.00005 is not an integer, but the answer key says it is i and iii. Is the answer key wrong or am I missing something?

#### soroban

##### Elite Member
Hello, dagr8est!

If x is an integer, which of the following could be x<sup>3</sup> ?

i) 1.25 x 10<sup>17</sup>
ii) 12.5 x 10<sup>-12</sup>
iii) 0.125 x 10<sup>-12</sup>

This is what I did.

i) 1.25(10<sup>17</sup>) = 125(10<sup>15</sup>) = [5(10<sup>5</sup>)]<sup>3</sup>, then x = 500000

ii) 12.5(10<sup>-12</sup>) = 125(10<sup>-13</sup>) = [5(10<sup>-13/3</sup>)]<sup>3</sup>, then x = 0.00023207...

iii) 0.125(10<sup>-12</sup>) = 125(10<sup>-15</sup>) = [5(10<sup>-5</sup>)]<sup>3</sup>, then x = 0.00005

I answered only i since 0.00005 is not an integer, but the answer key says it is i and iii.
Is the answer key wrong or am I missing something?
I see absolutely nothing wrong with your work.
Could there be a typo? .Did you copy the problem incorrectly?