The expression in the image is:

$(a^4 b c^3) \times (a^3 b^{-2} c)$

To simplify this expression, we'll use the laws of exponents, particularly the rule that states:

$x^m \times x^n = x^{m+n}$

Let's break down the multiplication:

1. For $a$: $a^4 \times a^3 = a^{4+3} = a^7$

2. For $b$: $b \times b^{-2} = b^{1+(-2)} = b^{-1} = \frac{1}{b}$

3. For $c$: $c^3 \times c = c^{3+1} = c^4$

Putting it all together, the simplified expression is:

$a^7 \times \frac{c^4}{b}$

Or, written in a different form:

$\frac{a^7 c^4}{b}$

Would you like any further details or explanations? Here are some related questions you might consider:

1. How would you simplify an expression with negative exponents in both the numerator and the denominator?
2. What are the rules for dividing exponents with the same base?
3. How would this expression change if one of the variables had a fractional exponent?
4. Can this expression be factored further?
5. How can this expression be used in a real-world application?

Tip: When multiplying expressions with the same base, always add the exponents, regardless of whether the exponent is positive or negative.