Math Problem Statement
Simplify. Write your answer using whole numbers and variables. 3pq 21p^2q^2
Solution
To simplify the expression , let's follow these steps:
Step 1: Factor out common terms
We have the terms:
- in the numerator.
- in the denominator.
Step 2: Simplify the constants
The constant terms are 3 and 21. We can simplify by dividing both the numerator and denominator by 3:
Step 3: Simplify the variables
Now, let's simplify the variables. For the -terms:
\frac{p}{p^2} = \frac{1}{p} \quad \text{(since p^2pp^{2-1} = p)}
For the -terms:
\frac{q}{q^2} = \frac{1}{q} \quad \text{(since q^2qq^{2-1} = q)}
Step 4: Combine everything
Now that we've simplified the constants and variables, we get:
Final Answer:
Would you like further details or explanations? Here are some related questions to explore:
- How do you simplify an expression with exponents and fractions?
- What is the rule for dividing terms with the same base?
- How do you factor constants in algebraic expressions?
- How do you simplify expressions involving negative exponents?
- Can you simplify expressions with more than two variables?
Tip: When simplifying fractions with variables, always cancel out common terms from the numerator and denominator first!
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Math Problem Analysis
Mathematical Concepts
Algebra
Simplification
Fraction Simplification
Exponents
Formulas
Fraction Simplification: (a * b) / (c * d) = (a/c) * (b/d)
Exponent Rule: p^m / p^n = p^(m-n)
Fraction Simplification of Constants: a/b = a/gcd(a, b) / b/gcd(a, b)
Theorems
Simplifying algebraic fractions
Exponent Division Rule
Suitable Grade Level
Grades 7-9
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