simplify cuberoot(3) / cuberoot(a^5*b^7*c^4)?

saying cuberoot works, or use old school algebra and raise the number or variable to (1/3)

as in ( a^5 * b^7 * c^4 ) ^ (1/3) [[ the parentheses are vital ]] or

3______ is how it can also look

V a^5

a*a*a = a^3 ... so the cuberoot of a^3 = a ... and in your case you have (a^2) left over inside the first ( )

>>EDIT at 4 a.m I do not like Drew's answer

because 8^(1/3) / 27^(1/3) = 2/3 = .666 whereas if you cube top and bottom

you get 8/27 = .296 repeating - - so I have given an example that he could be wrong

rules: when you raise a power to a power, you multiply exponents

when you multiply a base times a base you ADD the exponents

any number divided by itself = 1, and "1" times the original is the same function

so combining some steps

{a^(1/3) * b^(2/3) * c^(2/3)} * 3^(1/3) = { 3abbcc]^(1/3) }.......... .......... ........ = [3ab^2c^2]^(1/3)

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{ditto.......... .......... .......} * a^(5/3)*b^(7/3)*c^(4/3) = a^(6/3)*b^(9/3)*c^(6/3) = [a^2b^3c^2]

I believe that to be a valid answer [inside] {without having negative exponents in the numerator}, and I now verbally change my thumbs up for Drew to a thumbs down

Cubed root is written by placing a small 3 above the little outdash of a normal squared root, to get the cubed root out of the denominator just put the whole fraction to the power of 3, this will get rid of all the cube roots and leave you with [(3)➗((a^5*b^7*c^4))]