SOLUTION: Simplify. DO NOT USE negative exponents in the answer. (PLEASE EXPLAIN YOUR STEPS AS YOU GO - I have become so confused over this) x^-4 * x^ -7 thank you for your help in

Algebra ->  Equations -> SOLUTION: Simplify. DO NOT USE negative exponents in the answer. (PLEASE EXPLAIN YOUR STEPS AS YOU GO - I have become so confused over this) x^-4 * x^ -7 thank you for your help in      Log On


   

Question 624434: Simplify. DO NOT USE negative exponents in the answer. (PLEASE EXPLAIN YOUR STEPS AS YOU GO - I have become so confused over this)
x^-4 * x^ -7
thank you for your help in advance!
Found 3 solutions by Alan3354, ewatrrr, vleith:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E-4+%2A+x%5E-7
Multiply --> add exponents
= x%5E-11
= x%5E-11%2F1
Multiply NUM and DEN by x^11
= 1%2Fx%5E11

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Re: TY, Note: applying only ***** rules governing exponents to this problem: 

Listed others for future reference only.

x%5E%28-4%29%2Ax%5E%28-7%29+=+x%5E%28-11%29%2F1+    | %28+x%5Em+%29%28+x%5En+%29+=+x%5E%28+m+%2B+n+%29******

x%5E%28-11%29%2Ax%5E%2811%29%2Fx%5E%2811%29+ | Multiplying numerator and denomination by x^11

x%5E0%2Fx%5E%2811%29+=+1%2Fx%5E%2811%29          |a%5E0+=+1******

Not that You would go thru All this for every problem...

just wanted to show why according to the Rules for Exponents that x%5E%28-11%29+=+1%2Fx%5E%2811%29}



a%5E0+=+1******

%28+x%5Em+%29%28+x%5En+%29+=+x%5E%28+m+%2B+n+%29******



%28a%5Ep%29%5Eq+=+a%5E%28p%2Aq%29

root%28a%2Cp%29%2Aroot%28a%2Cq%29+=+root%28a%2Cp%2Aq%29

x%5Em%2Fx%5En=x%5E%28m-n%29

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E%28-4%29+%2A+x%5E%28-7%29 when multiplying powers of the same base, add exponents
x%5E%28-11%29 to change the sign of an exponent, move it 'up or down' and change the sign. Here is the math behind that trick
x%5E%28-11%29 =
x%5E%28-11%29+%2A+1+=
x%5E%28-11%29+%2A+%28%28x%5E11%29%2F%28x%5E11%29%29 =
%28X%5E%28-11%29+%2A+X%5E11%29%2F+%28x%5E11%29 =
%28x%5E0+%2F+x%5E11%29 x^0 is defined as equating to 1
1%2F%28x%5E11%29 which is simply 'moving the negative power from the numerator down to the denominator and changing the sign. The same thing can be done to move a negative exponent in the denominator up to the numerator.
Get it?