SOLUTION: (2s^-1T^3/6s^2T^-4)^-3 (That's 2s to the negative 1,t to the negative 3 over 6s to squared T to the power of negative 4 in parentheses and all of it to the power of negative

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: (2s^-1T^3/6s^2T^-4)^-3 (That's 2s to the negative 1,t to the negative 3 over 6s to squared T to the power of negative 4 in parentheses and all of it to the power of negative      Log On


   

Question 309197: (2s^-1T^3/6s^2T^-4)^-3
(That's 2s to the negative 1,t to the negative 3 over
6s to squared T to the power of negative 4 in parentheses
and all of it to the power of negative 3). I believe by other examples ^ is used as an "exponent" or power to equation and ( / ) is the same as a fraction. Sorry if I'm wrong, I'm still somewhat new to algebra.com.
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: %282s%5E-1%2AT%5E3%2F%286s%5E2%2AT%5E-4%29%29%5E-3 simplifies to 1%2F%28T%5E%287%29%2Fs%5E3%2F3%29%5E3
  • Text form: (2s^-1*T^3/(6s^2*T^-4))^-3 simplifies to 1/(T^(7)/s^3/3)^3
  • Cartoon (animation) form: simplify_cartoon%28+%282s%5E-1%2AT%5E3%2F%286s%5E2%2AT%5E-4%29%29%5E-3+%29
    For tutors: simplify_cartoon( (2s^-1*T^3/(6s^2*T^-4))^-3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around factor highlight_red%28+1%2F6+%29,highlight_red%28+1%2Fs%5E2+%29,highlight_red%28+1%2FT%5E-4+%29
It becomes .
Look at %28highlight_red%28+2+%29%2As%5E-1%2AT%5E3%2Fhighlight_red%28+6+%29%2Fs%5E2%2FT%5E-4%29%5E-3.
Factors 2 and 6 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes .
Look at %281%2Ahighlight_red%28+s%5E-1+%29%2AT%5E3%2F3%2Fhighlight_red%28+s%5E2+%29%2FT%5E-4%29%5E-3.
Reduce similar several occurrences of highlight_red%28+s%5E-1+%29 to highlight_green%28+s%5E%28-1-2%29+%29
It becomes %281%2Ahighlight_green%28+s%5E%28-1-2%29+%29%2AT%5E3%2F3%2FT%5E-4%29%5E-3.
Look at %281%2As%5E%28-1-2%29%2Ahighlight_red%28+T%5E3+%29%2F3%2Fhighlight_red%28+T%5E-4+%29%29%5E-3.
Reduce similar several occurrences of highlight_red%28+T%5E3+%29 to highlight_green%28+T%5E%283--4%29+%29
It becomes %281%2As%5E%28-1-2%29%2Ahighlight_green%28+T%5E%283--4%29+%29%2F3%29%5E-3.
Look at %281%2As%5E%28highlight_red%28+-1+%29-2%29%2AT%5E%283--4%29%2F3%29%5E-3.
Removed extra sign in front of -1
It becomes %281%2As%5E%28-highlight_green%28+1+%29-2%29%2AT%5E%283--4%29%2F3%29%5E-3.
Look at %281%2As%5E%28-1-2%29%2AT%5E%283-highlight_red%28+-4+%29%29%2F3%29%5E-3.
Removed extra sign in front of 4
It becomes %281%2As%5E%28-1-2%29%2AT%5E%283%2Bhighlight_green%28+4+%29%29%2F3%29%5E-3.
Look at %28highlight_red%28+1+%29%2As%5E%28-1-2%29%2AT%5E%283%2B4%29%2F3%29%5E-3.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes %28s%5E%28-1-2%29%2AT%5E%283%2B4%29%2F3%29%5E-3.
Look at %28s%5E%28-highlight_red%28+1+%29-highlight_red%28+2+%29%29%2AT%5E%283%2B4%29%2F3%29%5E-3.
Added fractions or integers together
It becomes %28s%5E%28highlight_green%28+-3+%29%29%2AT%5E%283%2B4%29%2F3%29%5E-3.
Look at %28s%5E%28-3%29%2AT%5E%28highlight_red%28+3+%29%2Bhighlight_red%28+4+%29%29%2F3%29%5E-3.
Added fractions or integers together
It becomes %28s%5E%28-3%29%2AT%5E%28highlight_green%28+7+%29%29%2F3%29%5E-3.
Look at %28s%5E%28highlight_red%28+-3+%29%29%2AT%5E%287%29%2F3%29%5E-3.
Removed extra sign in front of -3
It becomes %28s%5E%28-highlight_green%28+3+%29%29%2AT%5E%287%29%2F3%29%5E-3.
Look at %28highlight_red%28+s%5E%28-3%29+%29%2AT%5E%287%29%2F3%29%5E-3.
Negative power changes multiplication to division
It becomes %281%2Fhighlight_green%28+s%5E3+%29%2AT%5E%287%29%2F3%29%5E-3.
Look at highlight_red%28+%281%2Fs%5E3%2AT%5E%287%29%2F3%29%5E-3+%29.
Negative power changes multiplication to division
It becomes 1%2Fhighlight_green%28+%281%2Fs%5E3%2AT%5E%287%29%2F3%29%5E3+%29.
Look at 1%2F%28highlight_red%28+1+%29%2Fs%5E3%2AT%5E%287%29%2F3%29%5E3.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes 1%2F%28T%5E%287%29%2Fs%5E3%2F3%29%5E3.
Result: 1%2F%28T%5E%287%29%2Fs%5E3%2F3%29%5E3

Universal Simplifier and Solver


Done!


nd that simplifies to
27S%5E9%2FT%5E21