If (1/a^2 1/b^3)^6 = 432 find ab

Question

If (  1   1  )⁶ = 432 

      a²  b³ 

 

What is ab?

 

 

The answer given is 12, but I can't figure out how to get there.

Answer 1

does it give you any additional information beyond that? as written it is a single equation with two variables, so you would end up with a set of possible solutions, not a specific value. meaning that it's not possible to uniquely determine ab from the given information alone

Answer 2

Allie,

 

I think maybe your term on the right was supposed to be 1/432.  If so, then

 

[1/a²·b³]⁶ = 1/432

 

The left hand side simplifies to: [1/a³·b²] = 1/432

 

The right hand can be factored:  [1/a³·b²] = 1/(4·4·3·3·3) = 1/(4²·3³)

 

comparing terms we see that a³ = 3³ and b² = 4²

 

so a = 3 and b = 4, hence a·b = 12

Answer 3

Something is wrong with the equation. It is impossible to do this as written.