%5E-4.jpeg "(5t^3)^-4")
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
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Apply the negative exponent rule: (5t^3)^-4 = 1 / (5t^3)^4
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Apply the power of a product rule: 1 / (5t^3)^4 = 1 / (5^4 * (t^3)^4)
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Simplify further: 1 / (5^4 * (t^3)^4) = 1 / (625 * t^12)
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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.