## Tamilnadu State Board Class 9 Maths Solutions Chapter 2 Real Numbers Ex 2.5

Question 1.

Write the following in the form of 5^{n}:

(i) 625

(ii) \(\frac { 1 }{ 5 }\)

(iii) √5

(iv) \(\sqrt { 125 }\)

Solution:

(i) 625 = 5^{4}

(ii) \(\frac { 1 }{ 5 }\) = 5^{-1}

(iii) √5 = 5^{\(\frac { 1 }{ 2 }\)}

(iv) \(\sqrt { 125 }\)

\(=\sqrt{5^{3}}=\left(5^{3}\right)^{\frac{1}{2}}=5^{\frac{3}{2}}\)

Question 2.

Write the following in the form of 4^{n}:

(i) 16

(ii) 8

(iii) 32

Solution:

(i) 16 = 4^{2}

(ii) 8 = \(4^{1} \times 4^{\frac{1}{2}}=4^{1+\frac{1}{2}}=4^{\frac{3}{2}}\)

(iii) 32 = \(4 \times 4 \times 4^{\frac{1}{2}}=4^{2+\frac{1}{2}}=4^{\frac{5}{2}}\)

Question 3.

Find the value of

(i) (49)^{\(\frac { 1 }{ 2 }\)}

(ii) (243)^{\(\frac { 2 }{ 5 }\)}

(iii) 9^{\(\frac { -3 }{ 2 }\)}

(iv) (\(\frac { 64 }{ 125 }\))^{\(\frac { -2 }{ 3 }\)}

Solution:

Question 4.

Use a fractional index to write:

(i) √5

(ii) \(\sqrt[2]{7}\)

(iii) (\(\sqrt[3]{49}\))^{5}

((iv) \(\left(\frac{1}{\sqrt[3]{100}}\right)^{7}\)

Solution:

Question 5.

Find the 5^{th} root of

(i) 32

(ii) 243

(iii) 100000

(iv) \(\sqrt[1024]{3125}\)

Solution: