Exponent Rules and Polynomial Operations
Key exponent laws, polynomial vocabulary, and multiplication patterns from the lesson.
Keyboard Shortcuts
💡 Pro tip: Use keyboard shortcuts for faster studying!
Study Smart Tips for Exponent Rules and Polynomial Operations
Master these concepts using proven study techniques that actually work:
Active Recall
Test yourself before flipping each card to strengthen memory retention
Spaced Repetition
Review difficult cards more frequently than easy ones
Multiple Sessions
Break study time into shorter, focused sessions
Explain Aloud
Verbalize answers to reinforce understanding
Questions Covered in This Set
12 cards to master
Product rule for exponents
x^m · x^n = x^(m+n) — multiply like bases, add exponents. Example: x^3 · x^2 = x^5.
Quotient rule for exponents
x^m / x^n = x^(m−n) — divide like bases, subtract exponents. Example: x^5/x^2 = x^3.
Power of a power rule
(x^m)^n = x^(mn) — multiply the exponents. Example: (x^3)^2 = x^6.
Why is (3x)^2 = 9x^2 and not 3x^2?
Power of a product: the exponent applies to every factor inside the parentheses, so (3x)(3x) = 9x^2.
What does x^0 equal, and why?
x^0 = 1 (for x ≠ 0), because x^3/x^3 = 1 but the quotient rule gives x^0.
What does a negative exponent mean?
x^(−n) = 1/x^n — a reciprocal, not a negative number. So 2^(−3) = 1/8, not −8.
Simplify (−3x^2y^5)^3
−27x^6y^15: cube the coefficient (−3)^3 = −27 and multiply each exponent by 3.
The #1 error when subtracting polynomials
Forgetting to distribute the minus sign to EVERY term: (5x^2−2x+4) − (3x^2+6x−9) = 2x^2 − 8x + 13 (note +9).
FOIL: expand (x + 3)(x − 5)
x^2 − 5x + 3x − 15 = x^2 − 2x − 15.
Square of a binomial pattern
(a + b)^2 = a^2 + 2ab + b^2, so (x + 4)^2 = x^2 + 8x + 16 — the middle term is not optional.
Difference of squares pattern
(a + b)(a − b) = a^2 − b^2; middle terms cancel, so (x + 7)(x − 7) = x^2 − 49.
Define degree of a polynomial
The largest degree among its terms. For 4x^3 − 2x^2 + x − 9 the degree is 3.
