Math Problem Statement

Simplify the expression \(\frac{12p^5 a}{10p^2 a}\)

Solution

The expression in the image is:

12p5a10p2a\frac{12p^5 a}{10p^2 a}

To simplify this expression, let's break it down step by step:

  1. Simplifying the coefficients: 1210=65\frac{12}{10} = \frac{6}{5}

  2. Simplifying the variables:

    • For p5p^5 and p2p^2, we apply the rule of exponents: p5p2=p52=p3\frac{p^5}{p^2} = p^{5-2} = p^3.
    • The aa terms cancel each other out since aa=1\frac{a}{a} = 1.

Now, the simplified expression is:

65p3\frac{6}{5} p^3

Would you like more details or have any questions?

Here are 5 related questions to explore further:

  1. How do you simplify expressions involving exponents in different scenarios?
  2. What are the rules for simplifying rational expressions?
  3. How does multiplying or dividing powers with the same base work?
  4. How can you identify and cancel common factors in algebraic fractions?
  5. How would this process change if the terms in the denominator were different variables?

Tip: Always start by simplifying coefficients and then move on to variables, applying the rules of exponents.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Simplification

Formulas

\frac{p^m}{p^n} = p^{m-n}
\frac{a}{a} = 1

Theorems

Laws of Exponents
Simplifying Rational Expressions

Suitable Grade Level

Grades 8-10