Math Problem Statement
Solution
We are tasked with solving the following mathematical expression:
To begin, let's simplify both components of the product:
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Simplify :
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Simplify : [ \sqrt[5]{64} = \sqrt[5]{2^6} = 2^{6/5} ]
Now, we compute the product of these two simplified expressions:
Using the property of exponents, :
Next, express 4 as :
This matches with the answer choices. Since the form of the expression is where , this corresponds to option D:
Would you like further details or have any questions? Here are 5 related questions for practice:
- How do you simplify radical expressions involving prime factorization?
- What are the properties of exponents used to combine roots and powers?
- How do you simplify fractional exponents like ?
- What is the significance of multiplying powers of the same base?
- Can you explain the process of converting between radicals and fractional exponents?
Tip: Always simplify radical expressions by first looking for perfect squares or cubes!
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Math Problem Analysis
Mathematical Concepts
Exponents and Roots
Radical Expressions
Simplification of Expressions
Formulas
√a × √b = √(a × b)
Exponent Rules: a^m × a^n = a^(m+n)
Conversion between Radicals and Fractional Exponents: n√(a^m) = a^(m/n)
Theorems
Exponent Properties
Radical Simplification
Suitable Grade Level
Grades 9-12