Practice Flashcards
Flip to reveal answersState the three index laws for the same base.
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 10 Flashcards — Laws of exponents
Sign up free to track progress and get spaced-repetition review schedules.
Question
State the three index laws for the same base.
Answer
aᵐ × aⁿ = aᵐ⁺ⁿ (multiply→add); aᵐ ÷ aⁿ = aᵐ⁻ⁿ (divide→subtract); (aᵐ)ⁿ = aᵐⁿ (power of a power→multiply).
Question
What is a⁰?
Answer
a⁰ = 1 for any a ≠ 0. Example: 7⁰ = 1.
Question
What does a negative exponent mean?
Answer
A reciprocal: a⁻ⁿ = 1/aⁿ. Example: 2⁻³ = 1/8.
Question
What does a fractional exponent mean?
Answer
A root: a^(1/n) = ⁿ√a, and a^(m/n) = (ⁿ√a)ᵐ. Example: 8^(2/3) = (∛8)² = 4.
Question
Evaluate 27^(2/3).
Answer
Cube root first (∛27 = 3), then square: 3² = 9.
Question
Write 1/√x as a power of x.
Answer
√x = x^(1/2), and the reciprocal flips the sign: 1/√x = x^(−1/2).
Question
Given a^(2/3) = 4, find a.
Answer
Raise both sides to the reciprocal 3/2: a = 4^(3/2) = (√4)³ = 8.
Question
Can you combine 2³ × 3² with the index laws?
Answer
No — the laws need the SAME base. 2³ × 3² = 8 × 9 = 72 must be done directly.
Question
How do you solve an equation with aˣ and a²ˣ?
Answer
It is a quadratic in disguise: a²ˣ = (aˣ)², so substitute y = aˣ, solve the quadratic, then solve back for x.
Question
In a quadratic-in-aˣ, why reject y ≤ 0?
Answer
Because y = aˣ and a power is always positive — only positive y can give a real x. Discard zero or negative roots.
Read the notes
Full study notes for Laws of exponents
Topic 1.7 hub
Exponent & log laws
More from Topic 1.7
All flashcards in this topic
Math AA SL exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free