Final answer:
To simplify the given expression, subtract the smaller exponent from the larger exponent (15^18 / 15^3) to get 15^15, utilizing the law of exponents for division.
Step-by-step explanation:
The problem presented requires us to simplify an expression involving exponents, specifically dividing one exponential term by another. The laws of exponents tell us that when we divide powers with the same base, we subtract the exponents. This means that 15 raised to the power of 18 divided by 15 raised to the power of 3 simplifies to 1518 / 153 = 1518-3, which results in 1515.
This simplification uses the rule that states xa / xb = xa-b. Applying this rule makes the complex problem much more manageable and showcases the utility of understanding and applying exponent rules in mathematics.