1. The problem is to simplify or solve the expression $16x^3 - 2x^6$ using indices (exponents). 2. The expression is a subtraction of two terms with powers of $x$: $16x^3$ and $2x^6$. 3. We can factor out the common term with the lowest power of $x$, which is $x^3$, and also factor out the common numerical factor 2. 4. Factoring out $2x^3$ from both terms: $$16x^3 - 2x^6 = 2x^3(8 - x^3)$$ 5. This is the simplified form using indices and factoring. 6. If solving for $x$ when the expression equals zero, set: $$2x^3(8 - x^3) = 0$$ 7. This implies either: $$2x^3 = 0 \implies x^3 = 0 \implies x = 0$$ or $$8 - x^3 = 0 \implies x^3 = 8 \implies x = 2$$ 8. Therefore, the solutions are: $$x = 0 \text{ or } x = 2$$