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(4t^5)^3/2t^3

2 min read Jun 16, 2024
(4t^5)^3/2t^3

Simplifying the Expression: (4t^5)^(3/2) / 2t^3

This article will guide you through the process of simplifying the expression (4t^5)^(3/2) / 2t^3.

Understanding the Properties

Before we begin, let's recall some key properties of exponents:

  • (a^m)^n = a^(m*n) : This states that when raising a power to another power, we multiply the exponents.
  • a^m / a^n = a^(m-n): This rule tells us that when dividing powers with the same base, we subtract the exponents.

Simplifying the Expression

  1. Simplify the numerator:

    • Apply the first property: (4t^5)^(3/2) = 4^(3/2) * t^(5 * 3/2)
    • Simplify: 4^(3/2) = (2^2)^(3/2) = 2^3 = 8 and t^(5 * 3/2) = t^(15/2)

  2. Rewrite the expression:

    • Our expression now becomes: 8t^(15/2) / 2t^3

  3. Simplify by dividing the coefficients and subtracting exponents:

    • 8 / 2 = 4
    • t^(15/2) / t^3 = t^(15/2 - 3) = t^(9/2)

  4. Final Simplified Expression:

    • The simplified expression is: 4t^(9/2)

Conclusion

By applying the basic properties of exponents, we successfully simplified the expression (4t^5)^(3/2) / 2t^3 to 4t^(9/2). Remember, understanding the rules of exponents is crucial for tackling more complex algebraic expressions.

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