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!

Learn how to simplify the algebraic expression 6a^-1x5a/(3a^3)^0 step-by-step. This solution explores key exponent rules and algebraic concepts. Suitable for students in Grades 8-10.

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