Laws of Exponents & Rational Exponents (Grade 10) — Worksheet & Memo

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Grade 10 · Exponents

Laws of Exponents & Rational Exponents (Grade 10)

EXAM-STYLE CLASS TEST

Marks

Duration

55 minutes

Questions

Name:

Class:

Date:

Mark

/ 35

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
2⁻³ = …
(1)
A)18
B)−8
C)−6
D)−18
1.2
16^½ = …
(1)
A)4
B)8
C)32
D)116
1.3
8^2/3 = …
(1)
A)4
B)16
C)163
D)512
1.4
(3x²)³ = …
(1)
A)27x⁶
B)9x⁶
C)3x⁶
D)27x⁵
1.5
If 3^x = 81, then x = …
(1)
A)4
B)27
C)3
D)5
1.6
If 2^{x + 1} = 32, then x = …
(1)
A)4
B)5
C)15
D)16
1.7
x⁵ × x³x² = …
(1)
A)x⁶
B)x¹⁵
C)x⁴
D)x¹⁰
1.8
∛(x⁵) written with a rational exponent is …
(1)
A)x^5/3
B)x^3/5
C)x¹⁵
D)x²
1.9
5⁰ + 3⁻¹ = …
(1)
A)43
B)0
C)13
D)115
1.10
A colony starts with 3 bacteria and DOUBLES every hour. After 6 hours there are …
(1)
A)192
B)36
C)64
D)18

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[11 MARKS]

Simplify the following. Leave your answers with POSITIVE exponents.

2.1
3^{x + 1} − 3^x3^x
(4)
2.2
2^{x + 3}2^x
(3)
2.3
12a⁵b²4a²b⁶
(4)

Question 3

[14 MARKS]

Calculate the following WITHOUT a calculator, and solve the equations that follow.

3.1
16^−3/4
(4)
3.2
27^2/3
(3)
3.3
Solve for x: 5^2x = 125
(3)
3.4
Solve for x: 3^{3x − 1} = 27
(4)

TOTAL: 35 marks

This question paper consists of 3 questions.