Question 948373
Any number (except 0 itself) raised to the zero power is 1.  

Method 1: Using 0 exponent:
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{{{5^8*5^z=1}}}

Add the expontents of 5 on the left

{{{5^(8+z)=1}}}

Replace 1 on the right by {{{5^0}}}

{{{5^(8+z)=5^0}}}

Since the bases are the same non-1 positive number 5 on
both sides we may just equate the exponents:

{{{8+z=0}}}

{{{z=-8}}}

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Method 2:  Using negative exponent:

{{{5^8*5^z=1}}}

Divide both sides by {{{5^8}}}

{{{5^8*5^z/5^8=1/5^8}}}

{{{cross(5^8)*5^z/cross(5^8)=1/5^8}}}

Move the {{{5^8}}} from the bottom to the top
and change the sign of the exponent as {{{5^(-8)}}}

{{{5^z=5^(-8)}}}

Equate the exponents

{{{z = -8}}}

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Both ways are correct and give the same answer.  Take your pick.

Edwin</pre>