Because cubed root of b^27 = (b^27)^1/3
And using the power rule of exponents: (27)(1/3) = 9
you can test it. Say b=2
2^27 = 134217728
Using a calculator, you can find the cubed root of anything with the MATH button and selecting the cubed root. Using that option, you find that the cubed root of 134217728 is 512. (or set 134217728^(1/3) in your calculator)
2^9 = 512
Another way of seeing it:
cubed root of (b^27) = cubed root of [(b^9)(b^9)(b^9)]
= cubed root of [(b^9)^3]
27 = 3 * 3 * 3
The cube root of 27 is 3.
b^3 * b^3 * b^3 = b^27
This proves that the cube root of b^27 is b^3.
3rd root(b^27) = b^(27/3) = b^9.
1 byte9 (little 9)
∛b²⁷ = ∛(b³)³ = b³