Answer:
First and third options are equivalent, second and fourth options are not equivalent.
Step-by-step explanation:
Remember the relation:
[tex]a^n*a^m = a^{n + m}[/tex]
and:
[tex](a^n)^m = a^{n*m}[/tex]
We have the expression:
[tex]7^{1/5}*49^{7/5}[/tex]
We know that 49 = 7*7
Then we can write the above relation as:
[tex]7^{1/5}*49^{7/5} = 7^{1/5}*(7^2)^{7/5}[/tex]
We can use the second relationship from the above ones and write this as:
[tex]7^{1/5}*(7^2)^{7/5} = 7^{1/5}*7^{2*7/5} = 7^{1/5}*7^{14/5}[/tex]
Now we can use the first relationship to get:
[tex]7^{1/5}*7^{14/5} = 7^{1/5 + 14/5} = 7^{15/5} = 7^3 = 343[/tex]
Then:
The first option is equivalent.
The second option is not equivalent
The third option is equivalent.
The fourth option is not equivalent.
