Question

(24C) to the power of 2/3

Convert to radical
Please solve with steps/explanation
Thanks in advance!!

Answer 1

converting
`(24C)^{(2)/(3)}` into radical form we get
`\mathbf{4\sqrt[3]{(3C)^2} }`

Explanation:

We are given:
`(24C)^{(2)/(3)}`

And we need to convert into radical

We know that
`(1)/(3)=\sqrt[3]{x}`

Prime factors of 24 are: 2x2x2x3

Solving:

`(24C)^{(2)/(3)}\\=(2 * 2 * 2 *3* C)^{(2)/(3)}\\=(2^3)^{(2)/(3)}((3*C)^{(2)/(3)})\\=2^2((3*C)^{(2)/(3)})\\=4\sqrt[3]{(3C)^2}`

So, converting
`(24C)^{(2)/(3)}` into radical form we get
`\mathbf{4\sqrt[3]{(3C)^2} }`