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