1. **Stating the problem:** Simplify the expression $16x^3 - 2x^{-6}$ using the laws of indices. 2. **Recall the laws of indices:** - $a^m \times a^n = a^{m+n}$ - $\frac{a^m}{a^n} = a^{m-n}$ - $(a^m)^n = a^{mn}$ - $a^{-m} = \frac{1}{a^m}$ 3. **Analyze the expression:** The expression is $16x^3 - 2x^{-6}$. Since the terms have different powers of $x$, they cannot be combined by addition or subtraction. 4. **Rewrite the negative exponent:** Use the rule $a^{-m} = \frac{1}{a^m}$ to rewrite $x^{-6}$: $$ 16x^3 - 2x^{-6} = 16x^3 - \frac{2}{x^6} $$ 5. **Express as a single fraction:** To combine, find a common denominator $x^6$: $$ 16x^3 = \frac{16x^3 \times x^6}{x^6} = \frac{16x^{9}}{x^6} $$ So, $$ 16x^3 - 2x^{-6} = \frac{16x^{9}}{x^6} - \frac{2}{x^6} = \frac{16x^{9} - 2}{x^6} $$ 6. **Final simplified form:** $$ \boxed{\frac{16x^{9} - 2}{x^6}} $$ This is the simplified expression using indices rules.