Page 93 - Mathematics_Form_Two

Exponents and radicals

Example 5�2 (c) (–7) = (–7) × (–7) = 49
2
6
Write each of the following expressions (d) 2 = 2 × 2 × 2 × 2 × 2 × 2 = 64
in power form:
(a) 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 Example 5�5
⎛ 3 ⎞ ⎛ 3 ⎞ ⎛ 3 ⎞ ⎛ 3 ⎞ Express each of the following numbers
⎟
⎟
⎟
⎜
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(b) − ⎟ × − ⎟ × − ⎟ × − ⎟ ⎟ ⎟ ⎟ in exponential form using the indicated
⎜
⎜
⎜
⎜
⎟
⎟
⎟
⎜
⎜
⎜
⎜
⎟
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FOR ONLINE READING ONLY
⎝
4⎠
4⎠
⎝
⎝
4⎠
4⎠
⎝
(c) 10 × 10 × 10 × 10 × 10 × 10 base.
(d) (–7) × (–7) × (–7) (a) 64 in base 4
(b) 2701 in base 7
Solution (c) 125− in base 5−
(a) 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 = 6 8 Solution Mathematics for Secondary Schools
⎛
(b) 3 ⎞ ⎟ ⎛ ⎜ ⎜ 3 ⎞ ⎟ ⎛ ⎜ ⎜ 3 ⎞ ⎛ ⎜ ⎜ 3 ⎞ ⎛ ⎜ ⎜ 3 ⎞ ⎟ 4 (a) 64 444 4= ×× = 3
⎟
⎟
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− ⎟ × − ⎟ × − ⎟ × − ⎟× − ⎟
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⎟
⎟
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⎝ ⎜ 4⎠ ⎟ ⎟ ⎜ ⎝ 4⎠ ⎟ ⎟ ⎜ ⎝ 4⎠ ⎜ ⎝ 4⎠ ⎜ ⎝ 4⎠ ⎟ ⎟ (b) 2401 7 7 7 7= ××× = 7 4
(c) 10 × 10 × 10 × 10 × 10 × 10 = 10 6 (c) −125= (−5)×(−5)×(−5) = (−5) 3
(d) (–7) × (–7) × (–7) = (–7) 3
Engage in Activity 5.3 to explore
more about properties of bases to their
Example 5�3 exponents
Identify the power, base and exponent Activity 5�3: Analysing properties of
in each of the following exponential powers
numbers: 1. Write some numbers in power forms
3
(a) 4 (b) (–10) 6 (c) x n with negative or positive exponents
Solution and bases.
3
(a) 4 is the power, 4 is the base and 3 is 2. Use a calculator or any other
the exponent. mathematical software to analyse
6
(b) (–10) is the power, –10 is the base their effects in the final answer.
and 6 is an exponent. 3. Write your conclusion and share
n
(c) x is the power, x is the base and n is your findings.
an exponent.
Exercise 5�1
Example 5�4
1. Indentify the base and exponent in
Evaluate each of the following powers: each of the following exponential
4
3
(a) 5 (b) (–5) numbers:
17
4
2
6
(c) (–7) (d) 2 (a) 6 (b) 7
19
(c) (–10) (d) 3 800
Solution
0
4
(a) 5 = 5 × 5 × 5 × 5 = 625 (e) 6 2 (f) 50
(b) (–5) = (–5) × (–5) × (–5) = –125 (g) y 25 (h) 17 6
3
87
Student's Book Form Two
11/10/2024 20:12:12
MATHEMATIC F2 v5.indd 87 11/10/2024 20:12:12
MATHEMATIC F2 v5.indd 87