Question

Which of the following is equivalent to 5 sqrt 13^3

Answer 1

5 sqrt 13^3=5*(13^3)^(1/2)

5*(13*13^2)^(1/2)
5*13*(13)^(1/2)
65*(13)^(1/2)=65√13

the answer is 65√13

Answer 2

Correct answer is choice D)
`\left(13^{(3)/(5)}\right)`

Explanation:

Question says to find about which of the following is equivalent to
`\sqrt[5]{13^3}`

From comment sections, given choices are:

a)
`13^2`

b)
`13^15`

c)
`13^5/3`

d)
`13^3/5`

We see that each choice is in exponent form without any radical sign. So that means we also need to convert
`\sqrt[5]{13^3}` into exponent form.

We know that nth root is equivalent to power 1/n. So we can rewrite the given problem as:

`\sqrt[5]{13^3}`

`=\left(13^3\right)^{(1)/(5)}`

`=\left(13^{3\cdot(1)/(5)}\right)` {using formula
`\left(x^m\right)^n=x^(m\cdot n)`}

`=\left(13^{(3)/(5)}\right)`

Hence correct answer is choice D)
`\left(13^{(3)/(5)}\right)`.