H Algebra 2/Trig · Unit 1
Multiply, divide, and raise powers. Put coefficients together, then apply the exponent rules.
Product rule
Same base, multiply: add the exponents.
am · an = am + n
Quotient rule
Same base, divide: subtract the exponents.
aman = am − n
Power rule
A power raised to a power: multiply the exponents.
(am)n = amn
Coefficients and signs
Put numbers together and matching bases together. A negative base to an even power is positive. A negative base to an odd power stays negative.
One rule. Keep the same base.
The formula is
am · an = am + n
Same base, so add the exponents.
x⁴ · x⁷ = x4+7
x¹¹
Answer: x¹¹
The formula is
am · an = am + n
Same base, so add the exponents.
y³ · y⁸ = y3+8
y¹¹
Answer: y¹¹
The formula is
am · an = am + n
Same base, so add the exponents.
z⁵ · z² = z5+2
z⁷
Answer: z⁷
The formula is
(am)n = amn
A power raised to a power: multiply the exponents.
(a³)4 = a3 × 4
a¹²
Answer: a¹²
The formula is
aman = am − n
Same base, so subtract the exponents.
m¹⁰m⁴ = m10−4
m⁶
Answer: m⁶
The formula is
aman = am − n
Same base, so subtract the exponents.
w⁸w² = w8−2
w⁶
Answer: w⁶
Coefficients: numbers together, matching bases together.
Use the commutative property: numbers together, matching bases together.
5x³ · 2x⁴ = 5 · 2 · x³ · x⁴
5 · 2 = 10
The formula is
am · an = am + n
x³ · x⁴ = x3+4
10x⁷
Answer: 10x⁷
Use the commutative property: numbers together, matching bases together.
6y² · 4y⁵ = 6 · 4 · y² · y⁵
6 · 4 = 24
The formula is
am · an = am + n
y² · y⁵ = y2+5
24y⁷
Answer: 24y⁷
Use the commutative property: numbers together, matching bases together.
3z⁷ · 5z = 3 · 5 · z⁷ · z¹
3 · 5 = 15
The formula is
am · an = am + n
z⁷ · z¹ = z7+1
15z⁸
Answer: 15z⁸
Coefficients together. Matching bases together.
36a¹⁰6a⁴
366 = 6
The formula is
aman = am − n
a¹⁰a⁴ = a10−4
6a⁶
Answer: 6a⁶
Coefficients together. Matching bases together.
8b¹⁵24b⁵
824 = 13
The formula is
aman = am − n
b¹⁵b⁵ = b15−5
b¹⁰3
Answer: b¹⁰3
Coefficients together. Matching bases together.
20x⁹4x³
204 = 5
The formula is
aman = am − n
x⁹x³ = x9−3
5x⁶
Answer: 5x⁶
A product raised to a power, including a negative coefficient.
The formula is
(ab)n = anbn
(−2x⁵)3
(−2)3 = −8
The formula is
(am)n = amn
(x⁵)3 = x5 × 3
−8x¹⁵
Answer: −8x¹⁵
The formula is
(ab)n = anbn
(−4y³)2
(−4)2 = 16
The formula is
(am)n = amn
(y³)2 = y3 × 2
16y⁶
Answer: 16y⁶
The formula is
(ab)n = anbn
(−5z⁴)3
(−5)3 = −125
The formula is
(am)n = amn
(z⁴)3 = z4 × 3
−125z¹²
Answer: −125z¹²
The formula is
(ab)n = anbn
(−2a⁶)4
(−2)4 = 16
The formula is
(am)n = amn
(a⁶)4 = a6 × 4
16a²⁴
Answer: 16a²⁴
The formula is
(ab)n = anbn
(−3w²)2
(−3)2 = 9
The formula is
(am)n = amn
(w²)2 = w2 × 2
9w⁴
Answer: 9w⁴
Use the commutative property: numbers together, matching bases together.
2x³ · −3x⁴ = 2 · −3 · x³ · x⁴
2 · −3 = −6
The formula is
am · an = am + n
x³ · x⁴ = x3+4
−6x⁷
Answer: −6x⁷
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