Answer :
Sure, let's go through each task step by step:
### Task 1:
Determine the coefficient of the monomial [tex]\(-38b^{15}z^6\)[/tex].
- The coefficient is the numerical part of the monomial.
- For [tex]\(-38b^{15}z^6\)[/tex], the coefficient is [tex]\(-38\)[/tex].
### Task 2:
Write the literal part of the monomial [tex]\(-60a^8z^{10}\)[/tex].
- The literal part consists of the variables and their exponents.
- For [tex]\(-60a^8z^{10}\)[/tex], the literal part is [tex]\(a^8z^{10}\)[/tex].
### Task 3:
Convert the monomial [tex]\(-\frac{5}{13}b^{13}x^3a^9by^7a^4\)[/tex] to standard form with variables in alphabetical order.
- First, combine the like terms:
[tex]\(-\frac{5}{13}\times b^{13+1}\times x^3\times a^{9+4}\times y^7\)[/tex].
- Simplify to: [tex]\(-\frac{5}{13}a^{13}b^{14}x^3y^7\)[/tex].
- The standard form is: [tex]\(-\frac{5}{13}a^{13}b^{14}x^3y^7\)[/tex].
### Task 4:
Find which monomials are similar.
- Similar monomials have the exact same literal part, meaning the same variables with identical exponents.
- Let's examine:
1) [tex]\(2x^5y^2\)[/tex]
2) [tex]\(-9y^6xy\)[/tex]
3) [tex]\(x^2y^2x^3\)[/tex]
4) [tex]\(-15y^2x^5\)[/tex]
5) [tex]\(3xy^6\)[/tex]
- The variables and exponents in monomial 1) are [tex]\(x^5y^2\)[/tex].
- The variables and exponents in monomial 4) are [tex]\(y^2x^5\)[/tex].
- Hence, monomials 1) and 4) are similar.
### Task 5:
Find the sum of the similar monomials [tex]\(2z^3\)[/tex] and [tex]\(-9z^3\)[/tex].
- Add the coefficients of the monomials: [tex]\(2 + (-9) = -7\)[/tex].
- The sum of the similar monomials is [tex]\(-7z^3\)[/tex].
### Task 6:
Find the sum of similar monomials [tex]\(a^5b^5c^2\)[/tex] and [tex]\(7a^5b^5c^2\)[/tex].
- Add the coefficients: [tex]\(1 + 7 = 8\)[/tex].
- The sum of the similar monomials is [tex]\(8a^5b^5c^2\)[/tex].
These steps help understand how to approach each question involving coefficients, literal parts, standardization, similarity, and summation of monomials.
### Task 1:
Determine the coefficient of the monomial [tex]\(-38b^{15}z^6\)[/tex].
- The coefficient is the numerical part of the monomial.
- For [tex]\(-38b^{15}z^6\)[/tex], the coefficient is [tex]\(-38\)[/tex].
### Task 2:
Write the literal part of the monomial [tex]\(-60a^8z^{10}\)[/tex].
- The literal part consists of the variables and their exponents.
- For [tex]\(-60a^8z^{10}\)[/tex], the literal part is [tex]\(a^8z^{10}\)[/tex].
### Task 3:
Convert the monomial [tex]\(-\frac{5}{13}b^{13}x^3a^9by^7a^4\)[/tex] to standard form with variables in alphabetical order.
- First, combine the like terms:
[tex]\(-\frac{5}{13}\times b^{13+1}\times x^3\times a^{9+4}\times y^7\)[/tex].
- Simplify to: [tex]\(-\frac{5}{13}a^{13}b^{14}x^3y^7\)[/tex].
- The standard form is: [tex]\(-\frac{5}{13}a^{13}b^{14}x^3y^7\)[/tex].
### Task 4:
Find which monomials are similar.
- Similar monomials have the exact same literal part, meaning the same variables with identical exponents.
- Let's examine:
1) [tex]\(2x^5y^2\)[/tex]
2) [tex]\(-9y^6xy\)[/tex]
3) [tex]\(x^2y^2x^3\)[/tex]
4) [tex]\(-15y^2x^5\)[/tex]
5) [tex]\(3xy^6\)[/tex]
- The variables and exponents in monomial 1) are [tex]\(x^5y^2\)[/tex].
- The variables and exponents in monomial 4) are [tex]\(y^2x^5\)[/tex].
- Hence, monomials 1) and 4) are similar.
### Task 5:
Find the sum of the similar monomials [tex]\(2z^3\)[/tex] and [tex]\(-9z^3\)[/tex].
- Add the coefficients of the monomials: [tex]\(2 + (-9) = -7\)[/tex].
- The sum of the similar monomials is [tex]\(-7z^3\)[/tex].
### Task 6:
Find the sum of similar monomials [tex]\(a^5b^5c^2\)[/tex] and [tex]\(7a^5b^5c^2\)[/tex].
- Add the coefficients: [tex]\(1 + 7 = 8\)[/tex].
- The sum of the similar monomials is [tex]\(8a^5b^5c^2\)[/tex].
These steps help understand how to approach each question involving coefficients, literal parts, standardization, similarity, and summation of monomials.
