Final answer:
The function h(x) = (9x^4 - 3)^3 is expressed with only positive and negative exponents as 729x^12 - 27.
Step-by-step explanation:
To express the function h(x) = (9x^4 - 3)^3 using only positive and negative exponents, we follow the standard rules of raising an expression to a power. This involves raising both the numerical coefficient and the variable expression to the third power. In this case, the base 9x^4 is raised to the third power, which means we cube the 9 to get 729 and multiply the exponent 4 by 3 to get 12, resulting in a term 729x^12. The constant -3 is also raised to the third power, becoming -27. Therefore, the expression in its expanded form with only positive and negative exponents is 729x^12 - 27.