1
Algebra Notes
By Lona Matshingana
Concepts included
1. Exponent Rules
2. Simplifying using exponent rules
3. Simplifying radicals
4. Factoring
5. Rational Expressions
6. Solving Radical Equations
7. Absolute Value Equations
8. Interval Notation
9. Absolute value inequalities
10. Compound linear inequalities
11. Polynomial and Rational inequalities
12. Distance Formula
13. Midpoint Formula
14. Circles : Graphs and equations
15. Lines : Graphs and equations
16. Parallel and perpendicular lines
, 2
Exponent Rules
Here are some key exponent rules and examples:
Product Rule:
When multiplying terms with the same base, add the exponents:
x^m * x^n = x^(m+n)
Example: x^3 * x^5 = x^8
Quotient Rule:
When dividing terms with the same base, subtract the exponents:
x^m / x^n = x^(m-n)
Example: x^4 / x^2 = x^2
Power Rule:
When raising a term with an exponent to another power, multiply the exponents:
(x^m)^n = x^(m*n)
Example: (x^3)^4 = x^12
Zero Exponent Rule:
Any base raised to the 0 power equals 1:
x^0 = 1
Example: 5^0 = 1
Negative Exponent Rule:
A base raised to a negative exponent equals its reciprocal:
x^-n = 1 / x^n
Example: x^-3 = 1 / x^3
Product Rule with Negative Exponents:
When multiplying terms where one has a negative exponent, treat it as its reciprocal:
x^m * x^-n = x^(m-n)
Example: x^3 * x^-2 = x^(3-2) = x^1
, 3
So in summary, exponents allow you to shorthand multiplication, division, and repeated
multiplication of the same base. Following these rules avoids having to expand out all the
multiplications manually.
Algebra Notes
By Lona Matshingana
Concepts included
1. Exponent Rules
2. Simplifying using exponent rules
3. Simplifying radicals
4. Factoring
5. Rational Expressions
6. Solving Radical Equations
7. Absolute Value Equations
8. Interval Notation
9. Absolute value inequalities
10. Compound linear inequalities
11. Polynomial and Rational inequalities
12. Distance Formula
13. Midpoint Formula
14. Circles : Graphs and equations
15. Lines : Graphs and equations
16. Parallel and perpendicular lines
, 2
Exponent Rules
Here are some key exponent rules and examples:
Product Rule:
When multiplying terms with the same base, add the exponents:
x^m * x^n = x^(m+n)
Example: x^3 * x^5 = x^8
Quotient Rule:
When dividing terms with the same base, subtract the exponents:
x^m / x^n = x^(m-n)
Example: x^4 / x^2 = x^2
Power Rule:
When raising a term with an exponent to another power, multiply the exponents:
(x^m)^n = x^(m*n)
Example: (x^3)^4 = x^12
Zero Exponent Rule:
Any base raised to the 0 power equals 1:
x^0 = 1
Example: 5^0 = 1
Negative Exponent Rule:
A base raised to a negative exponent equals its reciprocal:
x^-n = 1 / x^n
Example: x^-3 = 1 / x^3
Product Rule with Negative Exponents:
When multiplying terms where one has a negative exponent, treat it as its reciprocal:
x^m * x^-n = x^(m-n)
Example: x^3 * x^-2 = x^(3-2) = x^1
, 3
So in summary, exponents allow you to shorthand multiplication, division, and repeated
multiplication of the same base. Following these rules avoids having to expand out all the
multiplications manually.
