Question

Which ones are Equivalent and Not equivalent?

Answer 1

Equivalent: 343;
`7^{(1)/(5)}*7^{(14)/(5)}`

Not Equivalent: 49;
`49^{(2)/(10)}*7^{(1)/(5)}`

Explanation:

In order to compare equivalent expressions, simplifying the initial expression is helpful:

`7^{(1)/(5) }*49^{(7)/(5)}` =
`7^{(1)/(5) }*7^{(14)/(5)}`

According to the laws of exponents, when multiplying with the same base, you add the exponents:

`7^{(1)/(5)+(14)/(5)}=7^{(15)/(5)}=7^(3)=343`