Math Problem Statement
Simplify $\left(\frac{3m^{-5}n^2}{4m^{-2}n^0}\right)^2\cdot\left(\frac{mn^4}{9n}\right)^2$
Solution
Let's simplify the given expression step by step:
Step 1: Simplify Each Fraction Inside the Parentheses
First Fraction:
- Since , we ignore it.
- Divide the powers of :
Thus, the first fraction simplifies to:
Second Fraction:
- Divide the powers of :
Thus, the second fraction simplifies to:
Step 2: Square Each Simplified Fraction
First Squared Expression:
Squaring each term:
Second Squared Expression:
Squaring each term:
Step 3: Multiply the Two Results
Multiply the numerators:
Multiply the denominators:
Thus, the expression simplifies to:
Step 4: Simplify the Coefficient
Thus, the final simplified expression is:
Or, writing with positive exponents:
Final Answer:
Would you like me to clarify any step or go into more details?
Related Questions:
- How do you simplify expressions with negative exponents?
- What are the laws of exponents and how do they apply to fraction simplifications?
- How do you handle complex fractions with variables in exponent form?
- What is the process of rationalizing expressions with negative exponents?
- How can exponent rules be applied in algebraic fraction simplifications?
Tip: Always simplify inside parentheses before applying exponent rules!
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Math Problem Analysis
Mathematical Concepts
Algebra
Exponent Rules
Fraction Simplification
Formulas
a^m / a^n = a^{m-n}
(a/b)^n = a^n / b^n
a^m * a^n = a^{m+n}
Theorems
Laws of Exponents
Fraction Multiplication
Suitable Grade Level
Grades 8-10
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