\((8x^3-9)^3=5832\)
Cube root each side.
∛5832 = 18. You can prime factorize to find this.
\(8x^3-9=18\)
Add 9 to each side.
\(8x^3=27\)
Divide by 8.
\(x^3=\frac{27}8\)
Cube root each side.
\(\boxed{x=\frac{3}2}\)
Note that radicals with an odd index (cube roots, 5th, 7th, etc.) don't leave a plus-minus...If there's an even number all of the negatives cancel, but if it's odd, it won't, just as with exponents.
