Unit 3: Exponents Practice Test
Math 9 Honours
Name: _________________________
Block: ____
Please initial this box to indicate you carefully read over your test and checked your work for simple
mistakes.
What I can do in this unit
Level
3-1
I can convert powers between exponential form, expanded form, and standard form
and evaluate using integer, fractions, and decimal bases.
3-2
I can use the exponent laws for products and quotients.
(add exponents for products of same bases, subtract for quotients)
3-3
I can use the power of a power exponent law and apply it to coefficients and variables.
(multiply exponents when taking the power of a power)
3-4
I can convert a negative power to a positive power and evaluate a zero power with
integer and fraction bases.
3-5
I can simplify and evaluate rational exponents including positive and negative
fractions.
Code
Value
N
MM
Not Yet Meeting Expectations
Minimally Meeting Expectations
M
Meeting Expectations
E
Exceeding Expectations
Description
I just don’t get it.
Barely got it, I need some prompting to help solve
the question.
Got it, I understand the concept without help or
prompting.
Wow, nailed it! I can use this concept to solve
problems I may have not seen in practice. I also get
little details that may not be directly related to this
target correct.
3-1: I can convert powers between exponential form, expanded form, and standard form and evaluate
using integer, fractions, and decimal bases.
Complete the table:
#
Exponential Form
1)
23
2)
−34
3)
−(−2)5
4)
−𝑥 5
Expanded Form
Standard Form
Cannot
Write each of the following in exponential form in as many ways as possible. Do not use a power of 1.
#
Standard Form
5)
125
6)
64
7)
100 000 000
8)
𝑥∙𝑥∙𝑥∙𝑥∙𝑥∙𝑥
Exponential Form
Evaluate each expression
9) 34 − 23 + 120
10) −52 + (−2)3
11) (5 − 20)0 − (−5)2
1 3
3 3
12) (2) ÷ (4)
Rewrite in standard form as a fraction or integer (no decimals)
13) −(−3)4
1 2
16) (−1 3)
5 4
3 3
14) (3)
15) (− 4)
17) (0.4)3
18) (1.5)4
3-2: I can use the exponent laws for products and quotients. Express answer in exponent form.
19) 52 ∙ 57
22)
36 ∙32 ∙3
33 ∙34
20)
𝑥9
23)
(−4)5 (−4)4
21) (−2)4 ∙ (−2)3
𝑥
24)
(−4)6 (−4)3
25) Rewrite each number with a base 2, then simplify.
𝑥 5 ∙𝑥∙𝑥 2
𝑥 4 ∙𝑥 7
256∙1024
64∙16
26) If a spaceship can travel at a rate of about 106 km per second, how long, in seconds, would it take to
reach a star that is 1015 km away?
27) The first floor of a (very) large apartment building has just 1 large apartment. The second floor has
2, the third 4. As you go higher, each floor has twice as many apartments as the floor below. If the
building has 24 floors, what is the total number of apartments in the entire building? Write your
answer in exponential form.
28) Consider the following tripling pattern: a very contagious virus infecting just one person is spread
to 3 others in just the first day. On day 2, 9 new people are infected. That means by day 2, 13 total
people have the virus! How many total people are infected by the virus after the 20th day? Write
your answer in exponential form.
3-3: I can use the power of a power exponent law and apply it to coefficients and variables.
29) (35 )2
3
32)
35)
31) (𝑎7 )3 (𝑎2 )4
30) (24 )5
2
(33 ) (36 )
33) (5𝑥 3 )4
3
34)
(34 )2
(6𝑥 12 )
3
(6𝑥 6 )2
4
36)
(256𝑥 5 ) (128𝑥 3 )
(1024𝑥 5 )3
6
(5𝑥 2 ) (5𝑥 3 )
7
(5𝑥 3 )4
3
37)
(243𝑥 2 ) (81𝑥 6 )
(2187𝑥 8 )2
4
3-4: I can convert a negative power to a positive power and evaluate a zero power with integer and
fraction bases.
38) 27𝑥 0
𝑥2
39) (−19𝑥)0
−4
41) (𝑦 −3 )
44) (2−3 )2 ∙ (22 )−4
40) −3−4
43) −(−4)−3
3−2
42) (3−5 )
45)
(23 )
−4
∙(2−5 )
(2−3 )3
−2
46)
(32𝑥 2 )
−1
(128𝑥 3 )
(2𝑥 4 )−3
−2
3-5: I can simplify and evaluate rational exponents including positive and negative fractions.
Simplify each and answer in standard form.
1
1
47) 164
49) 83
51) 810.25
2
50) 273
3
1
53) 16−2
32 −5
(243)
52)
5
2
57)
5
1 3
(− 8)
55) ( √16)−10
54) 25−2
1
56)
4
48) 325
24 −3
(81)
58) Solve for 𝑥:
42𝑥−1 = 1024