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Exponent rules

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Exponent rules

Product rule
am × an = am+n
Same base multiplied: add the powers.Lesson: Exponent rules →
Quotient rule
aman = am−n
Same base divided: take away the powers.Lesson: Exponent rules →
Power of a power
(am)n = am×n
A power raised to a power: multiply the powers.Lesson: Exponent rules →
Power of a product
(ab)n = an bn
Each factor gets the power.Lesson: Exponent rules →
Power of a quotient
(ab)n = anbn
Top and bottom both get the power.Lesson: Exponent rules →
Zero power
a0 = 1
Any number (not 0) to the power 0 is 1.Lesson: Exponent rules →
Negative power
a−n = 1an
A negative power means 1 over the positive power.Lesson: Exponent rules →
Rational exponent
amn = n√am = (n√a)m
The bottom of the power is the root, the top is the power.Lesson: Rational exponents →
Scientific notation
a × 10n, 1 ≤ a < 10
One digit before the point; n counts how far the point moved.Lesson: Scientific notation →

Powers and roots

Power
an = a × a × … × a
a multiplied by itself n times.Lesson: Powers, square roots, absolute value →
Square root
√a = b means b2 = a
The number that times itself gives a.Lesson: Powers, square roots, absolute value →
x² = k
x = √k or x = −√k
Two answers: a square of a negative is positive too.Lesson: Solve x² = 49 and x³ = 27 →
x³ = k
x = 3√k
One answer: the cube root keeps the sign.Lesson: Solve x² = 49 and x³ = 27 →

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