Explain why the following pair is not equal: (3x)^-1≠(3)/(x)

Question

Give reasons to why it is not equal. The -1 is a negative and the (3)/(x) is actually 3 over x

Answer 1

I am assuming this is asking why (3x)^-1 does not equal (3/x)?

 

It's because the -1 power applies to both the 3 and the x due to the parenthesis. So it is as follows: 

 

(3x)^-1 = (3^-1)*(x^-1) = (1/3)*(1/x) = (1/3x) 

 

(1/3x) does not equal (3/x)

Answer 2

On the right, we have 3 divided by x, 3/x.  On the left, we have the entire quantity 3x taken to the -1 power, (3x)^(-1).  So we must take the reciprocal of *both* the 3 and the x (not x alone).  What happens when we rewrite the left as a fraction?

Answer 3

Hi Shaukat - the rule for negative exponents is this:

 

A^-b = 1/A^b

 

An example of this is:  4^-2 = 1/4²  = 1/16

 

So (3x)^-1 = 1/(3x)¹ = 1/3x

 

1/3x does not equal 3/x