Question

If a is a real number and

m and n are positive integers, then a^m/n=m root a^n=m root a^n
a) True
b) False

Answer 1

The statement a^(m/n) = (m root a)^n is true because raising a number to a power and then taking a root is equivalent to the combined exponent/root operation.

Step-by-step explanation:

The question asks if the expression a^(m/n) is equal to the mth root of a^n, which can be written as (m root a)^n. According to the properties of exponents and roots, raising a number to a power m and then taking the nth root (or vice versa) is the same as raising the number to the power of m/n. Let's break it down: a^(m/n) means taking the nth root of a^m, and this is equivalent to taking the mth power of the nth root of a, or (m root a)^n. Therefore, the statement a^(m/n) = (m root a)^n is True.