Final answer:
To simplify the expression (-5)5 ÷ (-5)8, we subtract the exponents, then use the rule of negative exponents to get -1/125.
Step-by-step explanation:
To simplify the expression (-5)5 ÷ (-5)8, we can use the rule of exponentiation. When we divide two powers with the same base, we subtract the exponents. In this case, we have (-5)5 divided by (-5)8. The exponent of (-5)5 is 5 and the exponent of (-5)8 is 8. So, we subtract 8 from 5, giving us (-5)^(5-8) which simplifies to (-5)^(-3).
Now, we can use the rule of negative exponents. When we have a negative exponent, we can take the reciprocal of the base and change the sign of the exponent. So, (-5)^(-3) is equal to 1/(-5)^3, which is -1/125.
Therefore, the simplified form of (-5)5 ÷ (-5)8 is -1/125.
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