Sure, let's find the degree of each of the given algebraic expressions step-by-step.
### 9(a) [tex]\(-x^2 y^2 = 4\)[/tex]
- To find the degree of this expression, identify the exponents of each variable in the terms with variables.
- Here, one term is [tex]\(-x^2 y^2\)[/tex].
- The exponent of [tex]\(x\)[/tex] is 2 and the exponent of [tex]\(y\)[/tex] is 2.
- The degree of the term is [tex]\(2 + 2 = 4\)[/tex].
Thus, the degree of the expression is 4.
### 9(b) [tex]\(3x + 5y^2 - 3y^2 = 2\)[/tex]
- Simplify the expression first.
- Notice that [tex]\(5y^2 - 3y^2\)[/tex] cancels out to make [tex]\(0\)[/tex].
- So, we are left with the term [tex]\(3x\)[/tex].
- The exponent of [tex]\(x\)[/tex] is 1.
Thus, the degree of the expression is 1.
### 9(c) [tex]\(2x^2 y^4 + x^5 y^3 - x^2 y\)[/tex]
- Evaluate the degree of each term individually:
- For [tex]\(2x^2 y^4\)[/tex]: The exponents are 2 (for [tex]\(x\)[/tex]) and 4 (for [tex]\(y\)[/tex]), giving a term degree of [tex]\(2 + 4 = 6\)[/tex].
- For [tex]\(x^5 y^3\)[/tex]: The exponents are 5 (for [tex]\(x\)[/tex]) and 3 (for [tex]\(y\)[/tex]), giving a term degree of [tex]\(5 + 3 = 8\)[/tex].
- For [tex]\(-x^2 y\)[/tex]: The exponents are 2 (for [tex]\(x\)[/tex]) and 1 (for [tex]\(y\)[/tex]), giving a term degree of [tex]\(2 + 1 = 3\)[/tex].
- The highest degree among the terms is [tex]\(8\)[/tex].
Thus, the degree of the expression is 8.
### 9(d) [tex]\(a^4\)[/tex]
- This is a single term.
- The exponent of [tex]\(a\)[/tex] is 4.
Thus, the degree of the expression is 4.
### 9(e) [tex]\(-10 + 10x = 1\)[/tex]
- Simplify by removing constant terms.
- We are left with the term [tex]\(10x\)[/tex].
- The exponent of [tex]\(x\)[/tex] is 1.
Thus, the degree of the expression is 1.
### 9(f) [tex]\(7p^2 q^2 r - 17p^3 q^2 = S\)[/tex]
- Evaluate the degree of each term individually:
- For [tex]\(7p^2 q^2 r\)[/tex]: The exponents are 2 (for [tex]\(p\)[/tex]), 2 (for [tex]\(q\)[/tex]), and 1 (for [tex]\(r\)[/tex]), giving a term degree of [tex]\(2 + 2 + 1 = 5\)[/tex].
- For [tex]\(-17p^3 q^2\)[/tex]: The exponents are 3 (for [tex]\(p\)[/tex]) and 2 (for [tex]\(q\)[/tex]), giving a term degree of [tex]\(3 + 2 = 5\)[/tex].
- The highest degree among the terms is [tex]\(5\)[/tex].
Thus, the degree of the expression is 5.
### Summary
- (a) Degree: 4
- (b) Degree: 1
- (c) Degree: 8
- (d) Degree: 4
- (e) Degree: 1
- (f) Degree: 5
