Question

Rewire the rational exponent as a radical


`(5 * (3)/(4) ) (2)/(3)`
A.

`\sqrt[3]{5^(2) }`
B.

`\sqrt[12]{5}`
C.

`√(5)`
D.

`\sqrt[3]{5^(4) }`
​

Answer 1

`\large\boxed{\sqrt[3]{\left((15)/(4)\right)^2}}`

Explanation:

`a^(n)/(m)=\sqrt[m]{a^n}\\---------------------\\\\\left(5*(3)/(4)\right)^(2)/(3)=\left((5*3)/(4)\right)^(2)/(3)=\left((15)/(4)\right)^(2)/(3)=\sqrt[3]{\left((15)/(4)\right)^2}`

Answer:

`\large\boxed{C.\ \sqrt5}`

Explanation:

`\left(5^(3)/(4)\right)^(2)/(3)\\\\\text{Use}\ (a^n)^m=a^(nm)\\\\5^{(3)/(4)\cdot(2)/(3)}=5^{(1)/(2)\cdot(1)/(1)}=5^(1)/(2)=\sqrt[2]5=\sqrt5`