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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