The expression in the image is:

$-4x^2(6x^3)$

To simplify this using exponents, follow these steps:

Step 1: Distribute the constants

Multiply the constants $-4$ and $6$:

$-4 \times 6 = -24$

Step 2: Apply the exponent rule for multiplication

When multiplying powers of the same base, add the exponents. The exponents of $x$ in the expression are $2$ and $3$. Using the rule:

$x^a \cdot x^b = x^{a + b}$

So, $x^2 \cdot x^3 = x^{2+3} = x^5$.

Step 3: Combine the results

Now, multiply the constant $-24$ by $x^5$, resulting in:

$-24x^5$

Final Answer:

The simplified expression is:

$-24x^5$

Would you like more details on any of the steps? Here are some related questions to explore this topic further:

1. How do you apply the distributive property when simplifying expressions?
2. What are the rules for multiplying exponents with the same base?
3. How can you use negative exponents in similar expressions?
4. What is the difference between multiplying and dividing powers with the same base?
5. How can expressions with more than two terms be simplified using these rules?

Tip: When multiplying terms with the same base, always remember to add the exponents, not multiply them!