Which exponent makes the following statement true?
1/8^7 =8^?
one-seventh
negative one-seventh
7
negative 7
To make the statement true, we need to find the exponent (?) that satisfies the equation:
1/8^7 = 8^?
We know that taking an exponent to the negative is the same as taking the reciprocal of the base raised to the positive exponent. In other words, for any non-zero number 'a' and positive integer 'n':
1/a^n = a^(-n)
Applying this property to the given equation:
1/8^7 = 8^(-7)
Therefore, the exponent that makes the statement true is:
negative 7
So the correct choice is:
negative 7