A power contains two parts exponent and base.
We know 2 × 2 × 2 × 2 = 24, 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) 54.Solution:
54
= 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) -72.
Solution:
-72
= -(72) → 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
= 24
Therefore, required form = 24
(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