Problem 582 Divide the monomials. $$72 p^{... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 582

Divide the monomials. $$72 p^{12} \div 8 p^{3}$$

Short Answer

Expert verified

9p^9

Step by step solution

Identify the Monomials

The given problem is to divide two monomials: $72 p^{12}$ and $8 p^{3}$.

Divide the Coefficients

Divide the numerical coefficients: $72 \div 8$. This results in $9$.

Subtract the Exponents

For the variables, use the rule $a^m \div a^n = a^{m-n}$. In this case, for $p$, subtract the exponents: $12 - 3$. This results in $p^{9}$.

Combine Results

Combine the results of the coefficients and the variables: $9 p^9$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Polynomial Division

Dividing polynomials can look tricky, but it鈥檚 just breaking down each piece. In this example, we want to divide the monomials $72 p^{12}$ by $8 p^{3}$.

Start by identifying parts of the expression. The coefficients (the numbers in front of the variables) are 72 and 8. The variables are $p^{12}$ and $p^{3}$.

Always remember to handle coefficients separately from variables when dividing polynomials. After dividing the coefficients, you'll deal with the exponents by using exponent rules. Let's dive a bit deeper into those rules next.

Exponent Rules

When you divide variables with the same base, you subtract their exponents. This is a key rule for solving problems like this.

The rule can be described as:

$a^m \, \div \, a^n = a^{m-n}$

Here, we take the bases (in this case, $p$), and subtract the exponents.

So from $p^{12} \, \div \, p^{3}$, we subtract 3 from 12. That leaves us with $p^{9}$.

Remember, this rule only applies when the bases are the same. For other cases, additional steps might be required.

Arithmetic Operations

Arithmetic operations on coefficients are straightforward but important. Let's split this into manageable steps:

Step 1: Divide the coefficients

$72 \, \div \, 8 = 9$

Step 2: Apply the exponent rule for variables

$p^{12} \, \div \, p^{3} = p^{12-3} = p^{9}$

Combine both to get the final answer: $9 p^{9}$.

By breaking down operations step-by-step, even complex problems can be simplified and solved efficiently.

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91影视

Divide the monomials. $$72 p^{12} \div 8 p^{3}$$

Short Answer

Step by step solution

Identify the Monomials

Divide the Coefficients

Subtract the Exponents

Combine Results

Key Concepts

Polynomial Division

Exponent Rules

Arithmetic Operations

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