Math Problem Statement
Simplify the complex algebraic expression involving powers of numbers and variables, radicals, and fractions.
Solution
The given expression is quite complex. To solve it, we'll first break it down and simplify both the numerator and the denominator step by step.
The expression is:
Step 1: Simplify powers of numbers and variables in the numerator and denominator
Numerator
-
First part:
So the first part simplifies to: .
-
Second part:
- Simplifying inside the fraction:
- , so
So the second part simplifies to: .
- Simplifying inside the fraction:
Denominator
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Math Problem Analysis
Mathematical Concepts
Exponents and Powers
Algebraic Expressions
Simplifying Fractions
Radical Expressions
Formulas
Exponent Laws: a^m * a^n = a^(m+n), (a^m)^n = a^(mn)
Radical Expressions: (a^m)^n = a^(m/n)
Theorems
Properties of Exponents
Laws of Radical Exponents
Suitable Grade Level
Grades 9-12