Problem 583 Divide the monomials. $$-26 a^... [FREE SOLUTION]

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Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 583

Divide the monomials. $$-26 a^{8} \div\left(2 a^{2}\right)$$

Short Answer

Expert verified

-13 a^{6}

Step by step solution

Rewrite the Division

Rewrite the division of monomials as a fraction: \[-26 a^{8} \bigg/ 2 a^{2} \]

Simplify the Constants

Divide the coefficients (numbers) separately:\[-26 \bigg/ 2 = -13 \]

Apply the Exponent Rule

Use the rule for dividing powers with the same base, which states $a^m \bigg/a^n = a^{m-n}$:\[a^{8} \bigg/ a^{2} = a^{8-2} = a^{6} \]

Combine Simplified Parts

Combine the simplified parts to get the final answer:\[-13 \times a^{6} = -13 a^{6} \]

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Key Concepts

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

Exponent Rules

Exponents are a key concept when working with monomials. They represent repeated multiplication of a number or variable. For example, $a^8$ means $a$ multiplied by itself 8 times.

When dividing monomials, we often encounter rules for handling exponents. One important rule is that when you divide like bases, you subtract the exponents: \[ a^{m} \bigg/ a^{n} = a^{m-n} \]

In our exercise, we applied this rule to $a^{8} \bigg/ a^2$. We subtracted the exponents: $8 - 2 = 6$. Thus, $a^{8} \bigg/ a^2 = a^6$. Remember this rule whenever you are dividing variables with exponents, as it will simplify your calculations significantly.

Coefficients Division

Dividing the coefficients of monomials is straightforward. Coefficients are the numerical parts of the terms. In the given exercise, the coefficients are $-26$ and $2$.

To divide these, you simply perform standard division: $-26 \bigg/ 2 = -13$.

It's crucial not to confuse the coefficients with the variables or their exponents. Always divide the coefficients apart from the variables, then handle the exponents separately using the appropriate rules. This method ensures clarity and makes calculations easier.

Simplification of Monomials

Simplifying monomials involves combining the simplified coefficients and variables to get your final answer. In our example, we simplified the coefficient part to $-13$ and the variable part to $a^6$.

Combining these results gives us the simplified monomial: $-13 a^6$.

Here鈥檚 a simple checklist for simplifying monomials:

Rewrite the division as a fraction.
Divide the coefficients.
Apply exponent rules to the variables.
Combine the simplified coefficients and variables.

Following these steps will help you quickly and accurately simplify any monomial division problem.

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91影视

Divide the monomials. $$-26 a^{8} \div\left(2 a^{2}\right)$$

Short Answer

Step by step solution

Rewrite the Division

Simplify the Constants

Apply the Exponent Rule

Combine Simplified Parts

Key Concepts

Exponent Rules

Coefficients Division

Simplification of Monomials

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