how would you solve for x in the equation 4th root of 8 times cube root of 2 times square root of 8x equals 2?

Answer 1

I think this is what you mean:
4r - means 4th root.
3r - means 3rd root.
^½ - to power of a ½.

4r{ 8* 3r[2*√(8x)] } = 2
4r{ 8* 3r[2*√8 *√x)] } = 2
4r{ 8* 3r[2*√8 *√x)] } = 2
4r{ 8* 3r[2*√8 *x^½)] } = 2
4r{ 8* 3r[ 5∙656 854 249(x^½)] } = 2
4r{ 8*[ 1∙781 797 435(x^1/6)] } = 2
4r{ 14∙254 379 48 (x^1/6) } = 2
1∙943 063 882 (x^1/24) = 2
x^1/24 = 2 / 1∙943 063 882
x^1/24 = 1∙029 302 237 (get the power of 24).
x = 2

Answer 2

How would I solve it???
simply
express the roots as rational exponents of 2
combine terms
cancel terms
square both sides

ta-da!!!!