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Hello from MrBillDoesMath!

  1

Discussion:

Let's use exponents to rewrite the original equation:

The cube root of 7 =    7 ^ (1/3)

The square root of 7 = 7 ^ (1/2)

The remaining root = 7 ^ (5/6).

Substituting these values in the original equation gives:

( 7^(1/3) * 7 (1/2) )  / 7 ^ (5/6)  =

( 7 ^ (1/3 + 1/2) ) / 7 ^(5/6)

Now 1/3 + 1/2  = 2/6 + 3/6 = 5/6, so the numerator can be rewritten as

(7 ^ (5/6)) / ( 7 ^ (5/6)

But the numerator and denominator above are equal so the ratio is 1,

Thank you,

MrB