Question

If a is a real number and m and n are positive integers, then a^(m/n) = m square root of a^n = (m square root of a)^n.

A) True
B) False

Answer 1

The statement is false because the expressions represented incorrectly equate different root values and power values.

Step-by-step explanation:

The statement in question is whether a^(m/n) = m square root of a^n = (m square root of a)^n is true or false. We can analyze this by breaking it into parts and using the properties of exponents.

For the expression a^(m/n), this can be interpreted as the n-th root of a^m.

On the other hand, when we see m square root of a^n, it suggests that we are taking the m-th root of a^n, which is mathematically incorrect since it is mixing two different root values (m and n).

For the expression (m square root of a)^n, it implies taking the m-th root of a and then raising the result to the power of n, which is not equivalent to the original expression.

Therefore, the correct interpretation of a^(m/n) is the n-th root of a raised to the m-th power, or written as ((n-th root of a)^m).

Based on the properties of exponents and roots, the initial statement is False.