The expression provided is:

$4x^2 \times (-6x^7)$

We will multiply the coefficients and apply the laws of exponents.

Step-by-step solution:

1. Multiply the coefficients: $4 \times (-6) = -24$
2. Apply the exponent rule: When multiplying powers with the same base, add their exponents. So, for $x^2 \times x^7$, the exponents are added: $x^{2+7} = x^9$

Thus, the simplified expression is:

$-24x^9$

Would you like further clarification on any step or details about how the exponent rule works?

Related questions:

1. How do you multiply powers of the same base?
2. What is the rule for multiplying exponents with coefficients?
3. How do you distribute when multiplying more complex polynomials?
4. How does the power of a power rule differ from the multiplication of powers rule?
5. What happens when multiplying variables with different bases?

Tip:

Always ensure that you simplify both the numerical coefficients and the variables separately when multiplying algebraic expressions.