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Question
Find the value of the following:
(2−1 × 4−1) ÷ 2−2
Sum
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Solution
According to the rules of exponents,
(am)n = amn, a−m = 1/am
(2−1 × 4−1) ÷ 2−2
= [2−1 × {(2)2}−1] ÷ 2−2[Since 4 = 2 × 2 = 22]
= (2−1 × 2−2) ÷ 2−2 [∵(am)n = amn]
= 2−3 ÷ 2−2 [∵am × an = am + n]
= 2−3 + 2 = 2−1
1/2 [∵a−m = 1/am]
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