Question

Write the value of  \[\sqrt[3]{7} \times \sqrt[3]{49} .\]

Answer 1

We have to find the value of . `3sqrt7 xx 3sqrt49.`So,

`3sqrt7 xx 3sqrt49 = 3sqrt7 xx 3sqrt49.`

`= 7^(1/3) xx 7^(2 xx 1/3)`

`= 7^(1/3) xx 7^(2 /3)`

By using law rational exponents `a^m xx a^n = a^(m+n)` we get,

`3sqrt7 xx 3sqrt49 =7^(1/3) xx 7^(2 /3)`

`= 7^(1/3+2/3 )`

`= 7^(3/3)` = 7

Hence the value of `3sqrt7 xx 3sqrt49` is 7