Simplifying (5d^4)^3
This expression involves the power of a power, which is a common concept in algebra. Let's break down how to simplify it.
The Power of a Power Rule
The power of a power rule states that when raising a power to another power, you multiply the exponents. Mathematically, this is represented as:
(a^m)^n = a^(m*n)
Applying the Rule to our Expression
In our case, we have (5d^4)^3. Let's apply the power of a power rule:

Identify the bases and exponents:
 The base is 5d^4
 The exponent is 3

Multiply the exponents:
 (5d^4)^3 = 5^(43) * d^(43)

Simplify:
 5^(43) * d^(43) = 5^12 * d^12
Final Result
Therefore, the simplified form of (5d^4)^3 is 5^12 * d^12.
This expression can be further calculated if needed, but it is generally left in this form for simplicity.