Final answer:
The expression (x^2)^30 \cdot 4 simplifies to 4x^60 by multiplying the exponents (2 and 30) and then multiplying the result by the constant 4.
Step-by-step explanation:
When simplifying the expression (x^2)^30 \cdot 4, we first need to address the exponentiation of x^2 raised to the 30th power. According to the properties of exponents, when an exponent is raised to another exponent, we multiply the exponents together. Thus, (x^2)^30 simplifies to x^(2\times30) or x^60.
Next, we include the multiplication by 4 which is straightforward, resulting in our final simplified expression: 4x^60.
This demonstrates the importance of understanding how to use exponents and the rules for exponentiation, such as when raising a power to a power and when multiplying constants by variables with exponents.