Math Problem Statement
(49m².n²)³ : (7m⁸.n)⁵
Solution
We aim to simplify the expression:
Step 1: Expand the powers of each term.
For the numerator :
For the denominator :
Step 2: Write the expanded form.
The expression becomes:
Step 3: Simplify coefficients.
Since , . Substituting this:
Now, simplify .
Step 4: Simplify the powers of and .
For , .
For , .
Step 5: Combine results.
The simplified expression is:
Final Answer:
Would you like further clarification or examples? Here are some related questions for practice:
- Simplify .
- Expand and simplify .
- Simplify .
- If and , calculate the value of .
- How does the law of exponents simplify calculations with fractional bases?
Tip: Always simplify coefficients before handling exponents for more straightforward calculations.
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Math Problem Analysis
Mathematical Concepts
Algebra
Exponent Laws
Simplification of Rational Expressions
Formulas
Power of a product: (ab)^n = a^n * b^n
Law of exponents: a^m / a^n = a^(m-n)
Simplification of rational expressions
Theorems
Exponentiation rules
Simplification of rational expressions
Suitable Grade Level
Grades 8-10