The problem provided is:

$\text{Jika } a \neq 0, \text{ maka } \frac{(-2a)^3 \cdot (2a)}{(16a^4)^{\frac{1}{3}}} = \dots$

Step-by-Step Solution:

1. Simplify the numerator: $(-2a)^3 = (-2)^3 \cdot a^3 = -8a^3$ So the numerator becomes: $(-8a^3) \cdot (2a) = -8a^3 \cdot 2a = -16a^4$

2. Simplify the denominator: (16a^4)^{\frac{1}{3}} = 16^{\frac{1}{3}} \cdot (a^4)^{\frac{1}{3}} = 2^4^{\frac{1}{3}} \cdot a^{\frac{4}{3}} = 2a^{\frac{4}{3}}

3. Put everything together: Now the expression becomes: $\frac{-16a^4}{2a^{\frac{4}{3}}}$

4. Simplify the expression: Divide the constants: $\frac{-16}{2} = -8$ For the exponents of $a$: $a^4 / a^{\frac{4}{3}} = a^{4 - \frac{4}{3}} = a^{\frac{12}{3} - \frac{4}{3}} = a^{\frac{8}{3}}$

5. Final answer: $-8a^{\frac{8}{3}}$

Thus, the simplified expression is:

$\boxed{-8a^{\frac{8}{3}}}$

Would you like further clarification or details on any step?

Related Questions:

1. What are the rules for exponents when dividing terms with the same base?
2. How do we simplify expressions raised to fractional exponents?
3. Can this method be applied to negative bases in general?
4. How does the value of $a$ (if negative) affect the final result?
5. What is the cube root of a number, and how is it used here?

Tip:

When simplifying expressions with exponents, remember that you subtract the exponents when dividing powers with the same base.