Let's simplify the expression:

$(ab^0)(6a^{-4}b^3)(7a^2b)$

Step-by-step Breakdown:

1. Simplify $b^0$:

   • Recall that any non-zero number raised to the power of 0 is equal to 1: $b^0 = 1$ So, $ab^0 = a$.

   The expression now simplifies to: $a(6a^{-4}b^3)(7a^2b)$

2. Multiply the constants:

   • Multiply the constants 6 and 7: $6 \times 7 = 42$

   Now the expression becomes: $42a^{-4}b^3a^2b$

3. Simplify the powers of $a$ and $b$:

   • Combine the powers of $a$: $a^{-4} \times a^2 = a^{-4 + 2} = a^{-2}$

   • Combine the powers of $b$: $b^3 \times b^1 = b^{3 + 1} = b^4$

4. Final Expression: Now we have: $42a^{-2}b^4$

5. Simplify further if needed:

   • We can rewrite $a^{-2}$ as $\frac{1}{a^2}$.

   So, the fully simplified expression is: $\frac{42b^4}{a^2}$

Final Answer:

$\frac{42b^4}{a^2}$

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Would you like more details or have any further questions?

Here are some related questions for practice:

1. Simplify: $(x^3y^2)(2x^{-1}y^{-3})(5xy^4)$
2. What is the result when simplifying $(2a^3b^2)(3a^{-1}b^3)$?
3. Simplify the expression $(x^{-2}y^3)(x^4y^{-1})(2xy^{-2})$.
4. What is the product of $(3a^{-2}b^4)(2a^3b^{-2})$?
5. Simplify the expression $(4x^5y^{-3})(x^{-2}y^4)(2xy^{-1})$.

Tip: When multiplying terms with the same base, always add the exponents.