Math Problem Statement

Simplify the expression (16^(3/4) * 25^(1/2)) / (36^(1/2) * 4^(3/2))

Solution

The given expression simplifies to approximately 0.8330.833.

Would you like more details or have any questions? Here are some related questions to expand your understanding:

  1. What are the properties of exponents used in simplifying the given expression?
  2. How can we simplify expressions involving fractional exponents?
  3. What are some common applications of fractional exponents in real-world problems?
  4. Can the expression be simplified further using radical notation?
  5. How does changing the base numbers affect the result of the expression?

Tip: When working with exponents, remember that fractional exponents represent roots, e.g., x1/2x^{1/2} is the square root of xx.

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Math Problem Analysis

Mathematical Concepts

Exponents
Fractional Exponents
Radical Expressions

Formulas

a^(m/n) = n√(a^m)
Multiplication of exponents: a^m * a^n = a^(m+n)
Division of exponents: a^m / a^n = a^(m-n)

Theorems

Properties of Exponents
Laws of Exponents

Suitable Grade Level

Grades 9-12