There are many possible values of m that will make this sentence true: (7^0)^m = 1 Identify one value for m and explain your answer below

Answer 1

To solve the equation \((7^0)^m = 1\), we first need to simplify the left side.

1. Evaluate \(7^0\): Any nonzero number raised to the power of 0 is equal to 1. Therefore, we have: \[ 7^0 = 1 \]

2. Substituting into the equation: This transforms our original equation into: \[ (1)^m = 1 \]

3. Understanding the expression: Now, since \(1\) raised to any power \(m\) is always \(1\), the equation \((1)^m = 1\) is true for all real numbers \(m\).

Thus, \(m\) can be any real number. For example, \(m = 0\) is one specific value that satisfies the equation, since: \[ (7^0)^0 = 1^0 = 1 \]

In conclusion, one valid value for \(m\) is \(0\), but any real number will also satisfy the equation.