Final answer:
The expression (c⁵d⁴)³ simplifies to c¹⁵d¹² by raising each factor in the product to the power of three and multiplying the exponents by 3.
Step-by-step explanation:
To simplify the expression (c⁵d⁴)³, we can use the rule of integer powers and the properties of exponents. Raising a product to a power means each factor in the product is raised to that power. Thus, we apply the power to each variable separately.
We get:
c⁵ ³ = c³¹⁵
d⁴ ³ = d³¹²
We then multiply the exponent of the exponential term by 3:
5 × 3 = 15
4 × 3 = 12
Thus, the simplified expression is c¹⁵d¹².