could someone help me with math?

Question

Simplify this expression. If the answer contains exponents, all exponents should be positive.

(6st^-2/3s^2t^-5)^-4

Answer 1

Hi Seth,

 

Sometimes it's difficult to understand what's in the denominator.  It's helpful to use additional parentheses or brackets.  Having said this, this is how I'm interpreting your post.

 

6st^-2

-------   with the entire expression raised to the -4

3s²t^-5

 

This is equivalent to 

 

3s²t^-5

-------   with the entire expression raised to the +4

6st^-2

 

Now that +4 exponent can be distributed to each factor in the expression, giving us

 

3⁴s⁸t^-20

---------

6⁴s⁴t^-8

 

Now let's move the terms with the negative exponents so that they are positive

 

3⁴s⁸t⁸

--------

6⁴s⁴t²⁰

 

And simplify the variables

 

3⁴ s⁴

-------

6⁴ t¹²

 

Finally, 6 = (3)(2) so 64 = (3)⁴(2)⁴, making the expression

 

3⁴ s⁴
---------  
3⁴2⁴ t¹²

 

which reduces to

 

s⁴

--------   and further reduces to

2⁴ t¹²

 

   s⁴

-------

16t¹²