Exponents and Roots Basics
Key exponent rules, radical simplification, and common PSAT traps from this lesson.
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Questions Covered in This Set
12 cards to master
Multiplying like bases: x³ · x⁵ = ?
x⁸ — add the exponents when bases match.
Dividing like bases: x⁷ / x² = ?
x⁵ — subtract the exponents.
Power of a power: (x⁴)³ = ?
x¹² — multiply the exponents.
What is 7⁰? Why?
1. Any nonzero base to the zero power is 1 (since 7³/7³ = 7⁰ = 1).
What does a negative exponent mean? Evaluate 2⁻³.
It means reciprocal: x⁻² = 1/x². So 2⁻³ = 1/8, NOT −8.
Why is x² + x³ ≠ x⁵?
Exponent addition only applies to multiplying like bases, not to adding terms.
Compare (−3)² and −3².
(−3)² = 9; −3² = −9, because without parentheses the exponent applies only to the 3.
Write √x and ⁿ√(xᵐ) as exponents.
√x = x^(1/2) and ⁿ√(xᵐ) = x^(m/n).
Simplify √72.
√(36·2) = 6√2 — pull out the largest perfect square.
Is √(a+b) = √a + √b?
No. √(9+16) = 5 but 3+4 = 7. Roots distribute over multiplication/division only.
Simplify √(50x⁴).
√(25·2·x⁴) = 5x²√2.
If 2^x = 32, find x.
x = 5, since 32 = 2⁵ — rewrite both sides with the same base.
