what is the 4th root of 72x?!

To do this simplification you don't need to know the 4th root of 72x.
72x ^(-3/4) / 9x ^(1/3)
Divide the numeric coefficients:
8x ^(-3/4) / x ^(1/3)
Use the rules for dividing exponents:
8x^(-3/4 - 1/3)
Subtract the fractions:
8x^(-13/12)
or maybe:
8/x^(13/12)

72x^ (-3/4) divided by 9x^(1/3)

law of exponents; divide bases, subtract exponents.

(72/9) times x^(-3/4 - 1/3)

8 times x^ (-9/12 -4/12)

8 times x^ (-13/12)

8x^ -13/12

law of exponents; to the power of a negative, flip the fraction and make power positive.

8 times (x/1)^ -13/12

8 times (1/x)^ 13/12

8/1 times 1/x^13/12

8(1) / x^13/12

8 / x^(13/12)

can't simplify further.






if you need to simplify this expression using radical notation!

assuming expression is:

(72x)^ -3/4 divided by (9x) ^ 1/3

law of exponents; negative power, flip fraction make power positive.

(1/72x) ^3/4 divided by (9x) ^ 1/3

CANNOT COMBINE THESE EXPRESSIONS UNTIL THE FRACTIONS ARE proporational!

(1/72x) ^9/12 divided by (9x) ^4/12

^12√(1/72x)^9 divided by ^12√(9x)^4

^12√[1^9 / 72^9x^9] divided by ^12√[9^4 x^4]

^12√(1 /72^9x^9) divided by ^12√(6561x^4)

^12√[ (1/72^9x^9 divided by 6561x^4)

^12√[(1/72^9x^9 TIMES 1/6561x^4)

you then do the mutliplication, but to be honest, i don't think this is what you really want.