Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Exponents
2:18 minutes
Problem 33d
Textbook Question
Textbook QuestionMultiply or divide, as indicated. 15p^3/9p^2 * 12p/10p^3
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Simplifying Fractions
Simplifying fractions involves reducing the numerator and denominator by their greatest common factor (GCF). This process makes calculations easier and helps in understanding the relationship between the numbers. For example, in the fraction 15/9, both numbers can be divided by 3 to simplify it to 5/3.
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Multiplying Monomials
When multiplying monomials, you multiply the coefficients (numerical parts) and add the exponents of like bases. For instance, when multiplying 3p^2 by 4p^3, the result is 12p^(2+3) = 12p^5. This rule is essential for handling expressions involving variables raised to powers.
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Dividing Monomials
Dividing monomials requires dividing the coefficients and subtracting the exponents of like bases. For example, when dividing 12p^4 by 3p^2, you divide the coefficients (12/3 = 4) and subtract the exponents (p^(4-2) = p^2), resulting in 4p^2. This concept is crucial for simplifying expressions in algebra.
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