Powers (exponents)
Concept of
powers (exponents):
A power
contains two parts exponent and base.
We know 2 × 2 × 2 × 2 = 2
^{4}, where 2 is called the base and 4 is called the power or exponent or index of 2.
Reading Exponents
Examples on evaluating powers (exponents):
1. Evaluate each expression:
(i) 5
^{4}.
Solution:
5
^{4}
= 5 ∙ 5 ∙ 5 ∙ 5
→ Use 5 as a factor 4 times.
= 625
→ Multiply.
(ii) (3)
^{3}.
Solution:
(3)
^{3}
= (3) ∙ (3) ∙ (3)
→ Use 3 as a factor 3 times.
= 27
→ Multiply.
(iii) 7
^{2}.
Solution:
7
^{2}
= (7
^{2})
→ The power is only for 7 not for negative 7
= (7 ∙ 7)
→ Use 7 as a factor 2 times.
= (49)
→ Multiply.
= 49
(iv) (2/5)
^{3}
Solution:
(2/5)
^{3}
= (2/5) ∙ (2/5) ∙ (2/5)
→ Use 2/5 as a factor 3 times.
= 8/125
→ Multiply the fractions
Writing Powers (exponents)
2.
Write each number as the power of a given base:
(a) 16; base 2
Solution:
16; base 2
Express 16 as an exponential form where base is 2
The product of four 2’s is 16.
Therefore, 16
= 2 ∙ 2 ∙ 2 ∙ 2
= 2
^{4}
Therefore, required form = 2
^{4}
(b) 81; base 3
Solution:
81; base 3
Express 81 as an exponential form where base is 3
The product of four (3)’s is 81.
Therefore, 81
= (3) ∙ (3) ∙ (3) ∙ (3)
= (3)
^{4}
Therefore, required form = (3)
^{4}
(c) 343; base 7
Solution:
343; base 7
Express 343 as an exponential form where base is 7
The product of three (7)’s is 343.
Therefore, 343
= (7) ∙ (7) ∙ (7)
= (7)
^{3}
Therefore, required form = (7)
^{3}
Algebra 1
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