Answer Keys: Exponents

Student Concept Worksheet Answers

#	Answer	Explanation
1	x^7	Product rule: 5+2=7
2	y^5	Quotient rule: 9-4=5
3	a^15	Power rule: 3 times 5=15
4	1/9	3^(-2) = 1/3^2 = 1/9
5	1	Zero exponent rule
6	2^10 = 1024	(2^3)^2 = 2^6, then 2^6 times 2^4 = 2^10

Practice Worksheet Answers

Part A: Product Rule

#	Answer
1	x^7
2	y^9
3	a^6
4	2^7 = 128
5	m^12
6	b^9

Part B: Quotient Rule

#	Answer
7	x^5
8	y^7
9	a^0 = 1
10	5^4 = 625
11	m^8
12	z^5

Part C: Power Rule

#	Answer
13	x^10
14	y^12
15	a^12
16	2^12 = 4096
17	m^20
18	b^10

Part D: Zero/Negative Exponents

#	Answer	#	Answer
19	1	20	1
21	1/16	22	1/25
23	1/x^3	24	1/10 = 0.1

Part E: Mixed

#	Answer	Work
25	x^10	(x^3)^2=x^6, x^6 times x^4=x^10
26	y^2	(y^2)^3=y^6, y^8/y^6=y^2
27	a^18	a^4 times a^2=a^6, (a^6)^3=a^18
28	2^2 = 4	(2^3)^2=2^6, 2^6/2^4=2^2

Part F: Scientific Notation

#	Answer
29	35,000
30	0.0021
31	4.5 times 10^4
32	6.7 times 10^(-3)

Challenge

33

x^2 times y^3

(x^4 times y^3)^2 = x^8 times y^6. (x^2 times y)^3 = x^6 times y^3. Divide: x^(8-6) times y^(6-3) = x^2 times y^3

34

x = 5

2^5 = 32

FAST Practice Quiz Answers

1

B) x^8

Product rule: 5+3=8

2

B) y^6

Quotient rule: 10-4=6

3

B) a^12

Power rule: 4 times 3=12

4

Select: 5^0, x^0, (-7)^0

5^0 = 1 ✓
2^(-2) = 1/4 ✗
x^0 = 1 ✓
(-7)^0 = 1 ✓

5

C) 1/9

3^(-2) = 1/3^2 = 1/9

6

B) 2^8

(2^3)^2 = 2^6, then 2^6 times 2^2 = 2^8

Scoring Guide

Score	Interpretation	Action
6/6	Mastery	Ready for scientific notation and polynomial operations
4-5/6	Approaching	Review confused rules (product vs power, negative exponents)
2-3/6	Developing	Reteach with expanded form. Show why rules work.
0-1/6	Intervention	Start with meaning of exponents. Build from 2^3 = 2 times 2 times 2