Question : What is the value of ‘a’ in the below equation? {(5 × 5 × 5 × 5 × 5 × 5)5 × (5 × 5 × 5 × 5 × 5)8} ÷ (5 × 5) = (625)a
Option 1: 14
Option 2: 17
Option 3: 16
Option 4: 15
Correct Answer: 17
Solution : Given: {(5 × 5 × 5 × 5 × 5 × 5) 5 × (5 × 5 × 5 × 5 × 5) 8 } ÷ (5 × 5) = (625) a ⇒ {(5 6 ) 5 } × (5 5 ) 8 } ÷ (5 2 ) = (625) a ⇒ {5 30 × 5 40 } ÷ 5 2 = 625 a ⇒ 5 (30 + 40 – 2) = (5 4 ) a ⇒ 5 4a = 5 68 ⇒ 4a = 68 $\therefore$ a = 17 Hence, the correct answer is 17.
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