Question

What is x= if (8x^3-9)^3=5832

Answer 1

$(8x^3-9)^3=5832$

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.