The Laws of Exponents (Grade 8) — Worksheet & Memo

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Grade 8 · Exponents

The Laws of Exponents (Grade 8)

EXAM-STYLE CLASS TEST

Marks

Duration

1 hour

Questions

Name:

Class:

Date:

Mark

/ 39

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
x⁵ × x³ = …
(1)
A)x¹⁵
B)x⁸
C)x²
D)2x⁸
1.2
x¹⁰ ÷ x⁴ = …
(1)
A)x¹⁴
B)x⁶
C)x^2,5
D)x⁴⁰
1.3
(x³)⁴ = …
(1)
A)x⁷
B)x¹²
C)x⁸¹
D)4x³
1.4
7⁰ = …
(1)
A)0
B)1
C)7
D)undefined
1.5
(2x)³ = …
(1)
A)2x³
B)8x³
C)6x³
D)8x
1.6
x⁶ × x²x³ = …
(1)
A)x⁵
B)x⁴
C)x¹¹
D)x³⁶
1.7
3x² × 4x⁵ = …
(1)
A)7x⁷
B)12x⁷
C)12x¹⁰
D)7x¹⁰
1.8
Which one of the following is EQUAL to 2⁶?
(1)
A)2² × 2³
B)2² × 2⁴
C)2³ + 2³
D)(2²)²
1.9
x⁴ + x⁴ = …
(1)
A)x⁸
B)2x⁴
C)x¹⁶
D)2x⁸
1.10
(3x²y)² = …
(1)
A)6x⁴y²
B)9x⁴y²
C)9x²y²
D)3x⁴y²

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

[10 MARKS]

Simplify the following. Leave your answers in exponential form.

2.1
(3x²)³ × 2x⁴
(4)
2.2
16a⁶b⁵2a²b²
(3)
2.3
(2x³)² + 3x⁶
(3)

Question 3

[10 MARKS]

Calculate the following WITHOUT using a calculator.

3.1
2⁴ × 2³ ÷ 2⁵
(3)
3.2
A learner writes 3² + 3² = 3⁴. Show by calculation that the learner is wrong, and write down the correct answer.
(4)
3.3
Solve for x: 2^x = 32
(3)

Question 4

[9 MARKS]

Solve for x in each of the following.

4.1
2^x × 2^x+116 − 1 = 7
(5)
4.2
3^x+23 = 27
(4)

TOTAL: 39 marks

This question paper consists of 4 questions.

Statement	Reason