Simplifying (5t^3)^4
In mathematics, simplifying expressions is a crucial skill. Let's break down how to simplify the expression (5t^3)^4.
Understanding the Rules
This expression involves several key concepts:
 Exponents: An exponent indicates how many times a base is multiplied by itself. In this case, the base is (5t^3).
 Negative Exponents: A negative exponent means we take the reciprocal of the base raised to the positive version of the exponent.
 Power of a Product: When raising a product to a power, we apply the exponent to each factor individually.
The Steps

Apply the negative exponent rule: (5t^3)^4 = 1 / (5t^3)^4

Apply the power of a product rule: 1 / (5t^3)^4 = 1 / (5^4 * (t^3)^4)

Simplify further: 1 / (5^4 * (t^3)^4) = 1 / (625 * t^12)

Final Result: (5t^3)^4 = 1 / (625t^12)
Key Takeaways
 Simplifying expressions with negative exponents often involves taking the reciprocal.
 Remember to apply the exponent to each factor within the parentheses.
 The simplified expression represents the same value as the original expression, but in a more manageable form.