To simplify $\left(\frac{6}{3}\right)^3$ to the power of 6 and write the answer in exponent form, let's proceed step-by-step:

1. Simplify $\frac{6}{3}$: $\frac{6}{3} = 2$

2. Substitute and simplify $(2^3)^6$: $(2^3)^6 = 2^{3 \times 6} = 2^{18}$

So, the answer in exponent form is: $2^{18}$

Would you like more details on any of these steps?

Here are five related questions for further practice:

1. Simplify $\left(\frac{8}{2}\right)^2$ to the power of 5.
2. Simplify $\left(\frac{12}{4}\right)^3$ to the power of 4.
3. Simplify $\left(\frac{10}{5}\right)^5$ to the power of 2.
4. Simplify $(3^2)^4$ and express the answer in exponent form.
5. Simplify $\left(\frac{15}{3}\right)^4$ to the power of 3.

Tip: Remember that $(a^m)^n = a^{m \cdot n}$, which helps simplify nested exponents efficiently.