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omeli [17]
2 years ago
6

(36√6 + 6^5/2 / 108×12)^2=6^n , then find the value of n?

Mathematics
1 answer:
natali 33 [55]2 years ago
7 0

Step-by-step explanation:

<u>Given:</u> [{36√(6) + 6^(5/2)} / (108×12)]² = 6ⁿ

<u>Asked:</u> Find the value of n = ?

<u>EXPLANATION</u><u>:</u>

Given that:

[{36√(6) + 6^(5/2)} / (108×12)]² = 6ⁿ

⇛[{(6)² * (6)^(1/2) * (6)^(5/2}/(36 * 3 * 12)]² = 6ⁿ

⇛[{6² * 6^(1/2) * 6^(5/2)}/(36 * 36)]² = 6ⁿ

⇛[{6² * 6^(1/2) * 6^(5/2)}/(6*6 * 6*6)]² = 6ⁿ

⇛[{6² * 6^(1/2) * 6^(5/2)}/(6² * 6²)]² = 6ⁿ

⇛(6³⁻²)² = 6ⁿ

⇛(6¹)² = 6ⁿ

⇛6² = 6ⁿ

When an exponential has the same base on each side, then the exponents must be equal.

Therefore, n = 2.

<u>Answer</u><u>:</u> The Value of “n” for the given problem is 2.

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