Test Index

Delhi Police Constable Exam Model Paper 8

© examsnet.com

Question : 79 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:

By using the law of indices∶

Laws of Indices∶-

1-∶

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

2-∶

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

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

4-: (a)^{(1/m)} = \sqrt[m]{a}

5-: (a)^{-m} = \frac{1}{a^m}

6: (a)^{(m/n)} = \sqrt[n]{a^m}

7-∶

(a)^0 = 1

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

© examsnet.com

Go to Question:

Prev Question

Next Question