Problem 408 Divide the monomials. $$-88 y^... [FREE SOLUTION]

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Chapter 6: Problem 408

Divide the monomials. $$-88 y^{15} \div 8 y^{3}$$

Short Answer

Expert verified

-11 y^{12}

Step by step solution

Identify the coefficients

The coefficients are the numerical parts of the monomials. In this case, they are -88 and 8.

Divide the coefficients

Divide -88 by 8 to get the coefficient of the resulting monomial. $-88 \div 8 = -11$.

Subtract the exponents

For the variables, subtract the exponent of y^3 from y^{15}. This means, 15 - 3. So, the new exponent for y is 15 - 3 = 12.

Combine the results

Combine the results from the previous steps to write the final monomial: $-11 y^{12}$.

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Key Concepts

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

Coefficients

In algebra, a coefficient is the numerical part of a term. It is the number that multiplies the variable. For example, in the term -88y^{15}, -88 is the coefficient.
When we divide monomials, one of the first steps is to handle the coefficients.
In the provided exercise, we divide -88 by 8.
This calculation is straightforward. -88 divided by 8 gives us -11.
So the coefficient part of the new monomial is -11.
Understanding coefficients helps simplify complicated expressions.

Exponents

Exponents indicate how many times a number (the base) is multiplied by itself. In the term y^{15}, 15 is the exponent, and y is the base.
Exponents are crucial in monomial operations, especially in division.
When you divide monomials, you subtract the exponents of like bases.
For this exercise, you divide y^{15} by y^{3}. To do this, we subtract the exponents: 15 - 3, giving us 12.
So, the exponent part of the new monomial is y^{12}.
This rule of subtracting exponents applies to both simple and complex algebraic expressions.

Simplifying Expressions

Simplifying expressions is the process of reducing them to their simplest form. This usually makes them easier to work with.
In monomial division, we simplify by dividing coefficients and subtracting exponents.
For example, in the provided exercise -88 y^{15} divided by 8 y^{3}:

First, we handle the coefficients: -88 梅 8 = -11
Then, we deal with the exponents: 15 - 3 = 12
Finally, we combine the results: -11 y^{12}

The simplified expression is -11 y^{12}.
Simplifying helps us better understand and solve algebraic problems.
It reduces errors and makes checking work more straightforward.

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91影视

Divide the monomials. $$-88 y^{15} \div 8 y^{3}$$

Short Answer

Step by step solution

Identify the coefficients

Divide the coefficients

Subtract the exponents

Combine the results

Key Concepts

Coefficients

Exponents

Simplifying Expressions

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