Let's break down and simplify the expression:

$6a^{-1} \times 5a \div (3a^3)^0$

Step 1: Simplify the exponent in the denominator

Any term raised to the power of zero is equal to 1. So,

$(3a^3)^0 = 1$

Thus, the expression becomes:

$6a^{-1} \times 5a \div 1 = 6a^{-1} \times 5a$

Step 2: Simplify the multiplication of terms

Now, multiply the constants and handle the powers of $a$.

$6 \times 5 = 30$

For the powers of $a$, use the rule of exponents: $a^{-1} \times a^1 = a^{-1 + 1} = a^0$.

Since $a^0 = 1$, the entire expression simplifies to:

$30 \times 1 = 30$

Final Answer:

$30$

Let me know if you would like further clarification or have any questions! Here are some related problems you might want to try:

1. Simplify $7a^{-2} \times 2a^3$.
2. What is $(4b^{-1} \times 5b^2) \div b^3$?
3. Simplify $8x^{-2} \times x^5 \div x^2$.
4. Find the value of $9a^{-3} \times a^2 \times a^1$.
5. Simplify $(2c^3)^0 \times 4c^2$.

Tip: When multiplying terms with the same base, simply add the exponents!