SOLUTION: Can you please help me with this simplification problem? I can't figure out how to get it started and I can't find any examples in my book that are similar to it. (7e^(-4x))*2e

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Can you please help me with this simplification problem? I can't figure out how to get it started and I can't find any examples in my book that are similar to it. (7e^(-4x))*2e      Log On


   

Question 586632: Can you please help me with this simplification problem? I can't figure out how to get it started and I can't find any examples in my book that are similar to it.
(7e^(-4x))*2e^(2x)
Found 2 solutions by solver91311, eschwartz:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Just like multiplying any two factors where you have equal bases raised to a power. Add the exponents.

John

My calculator said it, I believe it, that settles it
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Answer by eschwartz(9) 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: %287e%5E%28-4x%29%29%2A2e%5E%282x%29 simplifies to 14%2Ae%5E%28-2%2Ax%29
  • Text form: (7e^(-4x))*2e^(2x) simplifies to 14*e^(-2*x)
  • Cartoon (animation) form: simplify_cartoon%28+%287e%5E%28-4x%29%29%2A2e%5E%282x%29+%29
    For tutors: simplify_cartoon( (7e^(-4x))*2e^(2x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28highlight_red%28+7%2Ae%5E%28-4%2Ax%29+%29%29%2A2%2Ae%5E%282%2Ax%29+%29.
Remove unneeded parentheses around factor highlight_red%28+7+%29,highlight_red%28+e%5E%28-4%2Ax%29+%29
It becomes highlight_green%28+7+%29%2Ahighlight_green%28+e%5E%28-4%2Ax%29+%29%2A2%2Ae%5E%282%2Ax%29.
Look at highlight_red%28+7+%29%2Ae%5E%28-4%2Ax%29%2Ahighlight_red%28+2+%29%2Ae%5E%282%2Ax%29.
Multiplied numerator integers
It becomes highlight_green%28+14+%29%2Ae%5E%28-4%2Ax%29%2Ae%5E%282%2Ax%29.
Look at 14%2Ahighlight_red%28+e%5E%28-4%2Ax%29+%29%2Ahighlight_red%28+e%5E%282%2Ax%29+%29.
Reduce similar several occurrences of highlight_red%28+e%5E%28-4%2Ax%29+%29 to highlight_green%28+e%5E%28%28-4%2Ax%29%2B%282%2Ax%29%29+%29
It becomes 14%2Ahighlight_green%28+e%5E%28%28-4%2Ax%29%2B%282%2Ax%29%29+%29.
Look at 14%2Ae%5E%28highlight_red%28+%28-4%2Ax%29+%29%2B%282%2Ax%29%29.
Remove unneeded parentheses around terms highlight_red%28+-4%2Ax+%29
It becomes 14%2Ae%5E%28-highlight_green%28+4%2Ax+%29%2B%282%2Ax%29%29.
Look at 14%2Ae%5E%28-4%2Ax%2Bhighlight_red%28+%282%2Ax%29+%29%29.
Remove unneeded parentheses around terms highlight_red%28+2%2Ax+%29
It becomes 14%2Ae%5E%28-4%2Ax%2Bhighlight_green%28+2%2Ax+%29%29.
Look at 14%2Ae%5E%28-highlight_red%28+4%2Ax+%29%2Bhighlight_red%28+2%2Ax+%29%29.
Eliminated similar terms highlight_red%28+-4%2Ax+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%28-4%2B2%29%2Ax+%29
It becomes 14%2Ae%5E%28highlight_green%28+%28-4%2B2%29%2Ax+%29%29.
Look at 14%2Ae%5E%28%28-highlight_red%28+4+%29%2Bhighlight_red%28+2+%29%29%2Ax%29.
Added fractions or integers together
It becomes 14%2Ae%5E%28%28highlight_green%28+-2+%29%29%2Ax%29.
Look at 14%2Ae%5E%28%28highlight_red%28+-2+%29%29%2Ax%29.
Removed extra sign in front of -2
It becomes 14%2Ae%5E%28%28-highlight_green%28+2+%29%29%2Ax%29.
Look at 14%2Ae%5E%28highlight_red%28+%28-highlight_red%28+2+%29%29%2Ax+%29%29.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes 14%2Ae%5E%28-highlight_green%28+2+%29%2Ax%29.
Result: 14%2Ae%5E%28-2%2Ax%29

Universal Simplifier and Solver


Done!