Write the following expression in simplified radical form

Question

Write the following expression in simplified radical form.

Assume that all of the variables in the expression represent positive real numbers.

Answer 1

24 = 3*2*2*2

14 / 3 = 4 remainder 2

so the cube root is 2 *x^5 * w*4 * cube_root( 3*w^2)

Answer 2

So, what's the third root of 24?

24 = 8 x 3 = 2³ × 3, sooooo ³√24 = 2√3

Taking a root of an exponent requires dividing the exponent by the root and leaving the remainder under the radical sign.

³√x¹⁵ = x⁵

³√w¹⁴ = w⁴√w²

³√24x¹⁵w¹⁴ = 2x⁵w^{4 3}√3w²