Answer:
Equivalent: 343; [tex]7^{\frac{1}{5}}*7^{\frac{14}{5}}[/tex]
Not Equivalent: 49; [tex]49^{\frac{2}{10}}*7^{\frac{1}{5}}[/tex]
Step-by-step explanation:
In order to compare equivalent expressions, simplifying the initial expression is helpful:
[tex]7^{\frac{1}{5} }*49^{\frac{7}{5}}[/tex] = [tex]7^{\frac{1}{5} }*7^{\frac{14}{5}}[/tex]
According to the laws of exponents, when multiplying with the same base, you add the exponents:
[tex]7^{\frac{1}{5}+\frac{14}{5}}=7^{\frac{15}{5}}=7^{3}=343[/tex]
