Question

Please help me with this math question!

Answer 1

1) Change radical forms to fractional exponents using the rule:
The nth root of "a number" = "that number" raised to the reciprocal of n.
For example
`\sqrt[n]{3} = 3^{ (1)/(n) }`.

The square root of 3 (
`√(3)`) = 3 to the one-half power (
`3^{ (1)/(2) }`).
The 5th root of 3 (
`\sqrt[5]{3}`) = 3 to the one-fifth power (
`3^{ (1)/(5) }`).

2) Now use the product of powers exponent rule to simplify:
This rule says
`a^(m) a^(n) = a^(m+n)`. When two expressions with the same base (a, in this example) are multiplied, you can add their exponents while keeping the same base.

You now have
`(3^{ (1)/(2) })*(3^{ (1)/(5) })`. These two expressions have the same base, 3. That means you can add their exponents:

`(3^{ (1)/(2) })(3^{ (1)/(5) })\\ = 3^{((1)/(2) + (1)/(5)) }\\ = 3^{(7)/(10)}`

3) You can leave it in the form
`3^{(7)/(10)}` or change it back into a radical
`\sqrt[10]{3^7}`

------

Answer:
`3^{(7)/(10)}` or
`\sqrt[10]{3^7}`