Final answer:
The expression 270 + 8g^12 does not have a factored form as it does not share a common factor nor fit a special factoring pattern. The closest operation related to the question is the rule of multiplying exponents when raising a power to a power.
Step-by-step explanation:
The question asks for the factored form of the expression 270 + 8g^12. None of the provided options (a), (b), (c), or (d) correctly factor the given expression. Factoring expressions typically involves finding common factors or using special factoring formulas. In the case of 270 + 8g^12, we do not have a common factor between the two terms and the expression does not fit any special factoring patterns such as a difference of squares, a sum of cubes, or a difference of cubes. Hence, the expression is already in its simplest form and cannot be factored further over the integers.
When discussing the multiplication of powers as shown in examples, it's important to note that the exponent refers to the number of times a number is multiplied by itself. For instance, (5^3)^4 means that 5 is multiplied by itself 3 times and that result is then raised to the fourth power, which is effectively 5^(3*4) or 5^12. This demonstrates the rule that when we raise a power to a power, we multiply the exponents.