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RRB Group-D Model Paper 15 with answers for online practice

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Question : 5 of 100

Marks: +1, -0

If

(\sqrt{3})^5 \times 9^2 = 3^n \times 3\sqrt{3}

, find the value of n.

5
6
7
8

Solution:

Given:

(\sqrt{3})^5 \times 9^2 = 3^n \times 3\sqrt{3}

Concept Used:

By using the law of indices∶

a^m \times a^n = a^{(m + n)}

a^m \div a^n = a^{(m - n)}

[(a^m)^n] = a^{mn}

a^{-m} = \frac{1}{a^m}

a^{m/n} = \sqrt[n]{a^m}

(a)0 = 1

Calculation:

The equation will be solved as:

(\sqrt{3})^5 \times 9^2 = 3^n \times 3\sqrt{3}

(\sqrt{3})^4 \times \sqrt{3} \times 9^2 = 3^n \times 3\sqrt{3}

⇒

9\sqrt{3} \times 9^2 = 3^n \times 3\sqrt{3}

⇒

3\sqrt{3} \times 3^5 = 3^n \times 3\sqrt{3}

⇒

3^5 = 3^n

⇒ n = 5

∴ Value of n is 5

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