To convert the exponential expression [tex]\( m^{\frac{7}{10}} \)[/tex] into its equivalent radical form, we need to understand the relationship between exponents and radicals. Specifically, the general form of an exponential expression can be rewritten in radical form as follows:
[tex]\[ m^{\frac{a}{b}} = \sqrt[b]{m^a} \][/tex]
Breaking down the given exponential expression [tex]\( m^{\frac{7}{10}} \)[/tex]:
1. The base [tex]\( m \)[/tex] is raised to a fractional exponent [tex]\(\frac{7}{10}\)[/tex].
2. The numerator [tex]\( 7 \)[/tex] represents the power to which [tex]\( m \)[/tex] is raised.
3. The denominator [tex]\( 10 \)[/tex] represents the index (or root) of the radical.
Therefore, according to the relationship between exponents and radicals, we can rewrite [tex]\( m^{\frac{7}{10}} \)[/tex] as follows:
[tex]\[ m^{\frac{7}{10}} = \sqrt[10]{m^7} \][/tex]
So, the exponential expression [tex]\( m^{\frac{7}{10}} \)[/tex] in radical form is:
[tex]\[ \sqrt[10]{m^7} \][/tex]
Given the options:
- [tex]\(\sqrt[10]{m^7}\)[/tex]
- [tex]\( m^8 \)[/tex]
- [tex]\( m^{-3} \)[/tex]
- [tex]\(\sqrt[7]{m^{10}}\)[/tex]
The correct equivalent radical form is:
[tex]\[ \sqrt[10]{m^7} \][/tex]
