Answer :
Rational exponents work like this:
[tex] a^{\frac{m}{n}} [/tex]
means that you have to raise [tex] a [/tex] to the [tex] m[/tex]-th power, and then take the [tex]n[/tex]-th root.
So, in your case, you are considering the 6th power of m, and then the 7th root. So, the expression is equivalent to
[tex] m^{\frac{6}{7}} [/tex]
The given expression i.e. [tex](\sqrt[7]{m}^6)[/tex] exponential expression should be equivalent to the radical expression i.e. [tex]m^{\frac{6}{7} }[/tex]
The following information should be considered:
- The rational exponent should be [tex]a^{\frac{m}{n} }[/tex]
- Here a should be raised to the m power and then took the n root.
Therefore, the first option is correct.
Learn more: brainly.com/question/17429689