In Exercises 1-8, Find The Degree Of The Monomial.1. $4g$2. $-\frac{4}{9}$3. $-1.75k^2$4. $23x^4$5. $s^8t$6. $8m^2n^4$7. $9xy^3z^7$8. $-3q^4rs^6$

by ADMIN 146 views

In mathematics, a monomial is an algebraic expression consisting of only one term, which can be a number, a variable, or a product of numbers and variables. The degree of a monomial is a measure of its complexity, and it is determined by the highest power of the variable(s) present in the expression. In this article, we will explore the concept of the degree of a monomial and apply it to various examples.

What is the Degree of a Monomial?

The degree of a monomial is the sum of the exponents of the variables present in the expression. For example, in the monomial x2y3x^2y^3, the degree is 2+3=52+3=5. This means that the highest power of the variable(s) in the expression is 5.

Example 1: Finding the Degree of a Monomial

4g4g

In this example, the monomial is 4g4g. Since there is only one variable, gg, and it has an exponent of 1, the degree of the monomial is 1.

Example 2: Finding the Degree of a Monomial

−49-\frac{4}{9}

In this example, the monomial is −49-\frac{4}{9}. Since there are no variables present, the degree of the monomial is 0.

Example 3: Finding the Degree of a Monomial

−1.75k2-1.75k^2

In this example, the monomial is −1.75k2-1.75k^2. Since the variable, kk, has an exponent of 2, the degree of the monomial is 2.

Example 4: Finding the Degree of a Monomial

23x423x^4

In this example, the monomial is 23x423x^4. Since the variable, xx, has an exponent of 4, the degree of the monomial is 4.

Example 5: Finding the Degree of a Monomial

s8ts^8t

In this example, the monomial is s8ts^8t. Since the variables, ss and tt, have exponents of 8 and 1, respectively, the degree of the monomial is 8+1=98+1=9.

Example 6: Finding the Degree of a Monomial

8m2n48m^2n^4

In this example, the monomial is 8m2n48m^2n^4. Since the variables, mm and nn, have exponents of 2 and 4, respectively, the degree of the monomial is 2+4=62+4=6.

Example 7: Finding the Degree of a Monomial

9xy3z79xy^3z^7

In this example, the monomial is 9xy3z79xy^3z^7. Since the variables, xx, yy, and zz, have exponents of 1, 3, and 7, respectively, the degree of the monomial is 1+3+7=111+3+7=11.

Example 8: Finding the Degree of a Monomial

−3q4rs6-3q^4rs^6

In this example, the monomial is −3q4rs6-3q^4rs^6. Since the variables, qq, rr, and ss, have exponents of 4, 1, and 6, respectively, the degree of the monomial is 4+1+6=114+1+6=11.

Conclusion

In conclusion, the degree of a monomial is a measure of its complexity, and it is determined by the highest power of the variable(s) present in the expression. By applying the concept of the degree of a monomial to various examples, we can gain a deeper understanding of this important mathematical concept.

Key Takeaways

  • The degree of a monomial is the sum of the exponents of the variables present in the expression.
  • The degree of a monomial can be determined by identifying the highest power of the variable(s) present in the expression.
  • The degree of a monomial is a measure of its complexity.

Further Reading

For further reading on the topic of monomials and their degrees, we recommend the following resources:

In this article, we will address some of the most frequently asked questions about the degree of a monomial.

Q: What is the degree of a monomial?

A: The degree of a monomial is the sum of the exponents of the variables present in the expression.

Q: How do I determine the degree of a monomial?

A: To determine the degree of a monomial, you need to identify the highest power of the variable(s) present in the expression. You can do this by looking at the exponent of each variable and adding them together.

Q: What is the degree of a monomial with no variables?

A: The degree of a monomial with no variables is 0.

Q: What is the degree of a monomial with one variable?

A: The degree of a monomial with one variable is equal to the exponent of that variable.

Q: What is the degree of a monomial with multiple variables?

A: The degree of a monomial with multiple variables is the sum of the exponents of all the variables.

Q: Can a monomial have a negative degree?

A: No, a monomial cannot have a negative degree. The degree of a monomial is always a non-negative integer.

Q: Can a monomial have a fractional degree?

A: No, a monomial cannot have a fractional degree. The degree of a monomial is always an integer.

Q: How do I simplify a monomial with a variable raised to a power?

A: To simplify a monomial with a variable raised to a power, you need to multiply the coefficient by the variable raised to the power.

Q: Can a monomial have a coefficient?

A: Yes, a monomial can have a coefficient. The coefficient is a number that is multiplied by the variable(s) in the monomial.

Q: How do I add or subtract monomials?

A: To add or subtract monomials, you need to combine like terms. Like terms are monomials with the same variable(s) raised to the same power.

Q: Can a monomial be a polynomial?

A: Yes, a monomial can be a polynomial. A polynomial is an expression consisting of one or more terms, and a monomial is a term with one variable or constant.

Conclusion

In conclusion, the degree of a monomial is an important concept in algebra that helps us understand the complexity of an expression. By answering some of the most frequently asked questions about the degree of a monomial, we hope to have provided a better understanding of this concept.

Key Takeaways

  • The degree of a monomial is the sum of the exponents of the variables present in the expression.
  • The degree of a monomial can be determined by identifying the highest power of the variable(s) present in the expression.
  • A monomial can have a coefficient, and it can be a polynomial.

Further Reading

For further reading on the topic of monomials and their degrees, we recommend the following resources: