My algebra book says that a^-n is equal to 1/a^n, which is equal to (1/a)^n. Does that then mean that a^n/m would be equal to (a/m)^n? Thank you very much.
No.
an/m
means mth root (an)
factor 900 into its prime factors
To answer your question, we need to understand the rules of exponents. In general, when dealing with exponents, we have two properties that we can use:
1. Negative exponent property: a^(-n) = 1 / a^n. This property states that if we have a negative exponent on a base, we can rewrite it as the reciprocal of the base raised to the positive exponent.
2. Power of quotient property: (a / b)^n = a^n / b^n. This property states that when we have a quotient raised to a power, we can distribute the power to both the numerator and the denominator.
Now, let's consider the expression a^(n/m). According to the power of quotient property, we can rewrite it as (a^n)^(1/m), since raising a number to the power of 1/m is the same as taking the mth root of the number. Therefore, we have:
a^(n/m) = (a^n)^(1/m)
Now, if we apply the negative exponent property to a^n, we get:
(a^n)^(1/m) = (1 / a^(-n))^(1/m)
Applying the power of quotient property again, we can write it as:
(1 / a^(-n))^(1/m) = (1^(1/m)) / (a^(-n))^(1/m)
Simplifying further, we have:
(1^(1/m)) / (a^(-n))^(1/m) = 1 / (a^(-n/m))
Therefore, a^(n/m) is equal to 1 / (a^(-n/m)).
In conclusion, a^(n/m) is not equal to (a/m)^n, but rather equal to 1 / (a^(-n/m)).