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

Answer:

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

Step-by-step 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:

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

$=\left(13^3\right)^{\frac{1}{5}}$

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

$=\left(13^{\frac{3}{5}}\right)$

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