Math Problem Statement

Simplify. Write your answer using whole numbers and variables. 3pq 21p^2q^2

Solution

To simplify the expression 3pq21p2q2\frac{3pq}{21p^2q^2}, let's follow these steps:

Step 1: Factor out common terms

We have the terms:

  • 3pq3pq in the numerator.
  • 21p2q221p^2q^2 in the denominator.

Step 2: Simplify the constants

The constant terms are 3 and 21. We can simplify 321\frac{3}{21} by dividing both the numerator and denominator by 3:

321=17\frac{3}{21} = \frac{1}{7}

Step 3: Simplify the variables

Now, let's simplify the variables. For the pp-terms:

\frac{p}{p^2} = \frac{1}{p} \quad \text{(since p^2dividedbydivided bypgivesgivesp^{2-1} = p)}

For the qq-terms:

\frac{q}{q^2} = \frac{1}{q} \quad \text{(since q^2dividedbydivided byqgivesgivesq^{2-1} = q)}

Step 4: Combine everything

Now that we've simplified the constants and variables, we get:

3pq21p2q2=17pq\frac{3pq}{21p^2q^2} = \frac{1}{7pq}

Final Answer:

17pq\frac{1}{7pq}

Would you like further details or explanations? Here are some related questions to explore:

  1. How do you simplify an expression with exponents and fractions?
  2. What is the rule for dividing terms with the same base?
  3. How do you factor constants in algebraic expressions?
  4. How do you simplify expressions involving negative exponents?
  5. 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