SOLUTION: For what value is z is {{{5^8*5^z=1}}} Please help me I just know that is has to do with Negative and Zero powers because that is our leason we are on.

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: For what value is z is {{{5^8*5^z=1}}} Please help me I just know that is has to do with Negative and Zero powers because that is our leason we are on.      Log On


   

Question 948373: For what value is z is 5%5E8%2A5%5Ez=1
Please help me I just know that is has to do with Negative and Zero powers because that is our leason we are on.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Any number (except 0 itself) raised to the zero power is 1.
Method 1: Using 0 exponent:
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5%5E8%2A5%5Ez=1
Add the expontents of 5 on the left
5%5E%288%2Bz%29=1
Replace 1 on the right by 5%5E0
5%5E%288%2Bz%29=5%5E0
Since the bases are the same non-1 positive number 5 on
both sides we may just equate the exponents:
8%2Bz=0
z=-8
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Method 2: Using negative exponent:
5%5E8%2A5%5Ez=1
Divide both sides by 5%5E8
5%5E8%2A5%5Ez%2F5%5E8=1%2F5%5E8
cross%285%5E8%29%2A5%5Ez%2Fcross%285%5E8%29=1%2F5%5E8
Move the 5%5E8 from the bottom to the top
and change the sign of the exponent as 5%5E%28-8%29
5%5Ez=5%5E%28-8%29
Equate the exponents
z+=+-8
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Both ways are correct and give the same answer. Take your pick.
Edwin