HELP W/ ACT PREP QUESTION: Which of the following equations expresses c in terms of a for all real numbers, a, b, and c such that a^3=b and b^2=c?
1.) c=a^6
2.) c= a^5
3.) c=2a^3
4.) c=1/2 a
5.) c= a

Question

HELP W/ ACT PREP QUESTION: Which of the following equations expresses c in terms of a for all real numbers, a, b, and c such that a^3=b and b^2=c?
1.) c=a^6
2.) c= a^5
3.) c=2a^3
4.) c=1/2 a
5.) c= a

iwanttogotostanford · Answer

@Vocaloid @zepdrix @pooja195

iwanttogotostanford · Answer

@Nnesha

jim_thompson5910 · Answer

replace b with a^3

b^2 = c
(b)^2 = c
(a^3)^2 = c

I'll let you finish up

iwanttogotostanford · Answer

@jim_thompson5910 im not sure how to finish!  Also, what was your reassigning in knowing how to do that??

jim_thompson5910 · Answer

I replaced b with a^3 because the first equation is a^3 = b or b = a^3

a^3 is the same as b, which is why the replacement can be done

jim_thompson5910 · Answer

you'll use 

$$\LARGE (x^a)^b = x^{a*b}$$

jim_thompson5910 · Answer

eg:

$$\LARGE (x^8)^5=x^{8*5}=x^{40}$$

iwanttogotostanford · Answer

is that ALg. 2??

jim_thompson5910 · Answer

yeah you'd most likely learn that in alg 2

jim_thompson5910 · Answer

maybe alg 1, it depends on the teacher

iwanttogotostanford · Answer

so it would be choice number 1?

iwanttogotostanford · Answer

@jim_thompson5910

jim_thompson5910 · Answer

yes, c = a^6