Which exponent makes this statement true? One fifth to the ninth power equals five to what power?
A) 9
B)-9
C) 1/9
D)-1/9
To solve this problem, we need to use the property of exponents that states "a^(m*n) = (a^m)^n".
Given the expression (1/5)^9, we want to find the exponent that would make it equal to 5^x.
First, we can simplify (1/5)^9:
(1/5)^9 = 1^9 / 5^9 = 1/5^9
Now, let's compare this to 5^x:
1/5^9 = 5^x
To make the bases the same, we can rewrite 5^x as 5^(x*1):
1/5^9 = 5^(x*1)
By using the property of exponents mentioned earlier, we can also rewrite this as:
1/5^9 = (5^1)^x = 5^x
Now we can set the exponents equal to each other:
x = 9
Therefore, the answer is A) 9.