## MP Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.6

Question 1.

find:

- 64
^{\(\frac{1}{2}\)} - 32
^{\(\frac{1}{5}\)} - 125
^{\(\frac{1}{3}\)}

Solution:

- 64
^{\(\frac{1}{2}\)}= (8^{2})^{\(\frac{1}{2}\) } - 32
^{\(\frac{1}{5}\)}= (2^{5})^{\(\frac{1}{5}\) } - 125
^{\(\frac{1}{3}\)}=(5)^{3x\(\frac{1}{2}\)}= 5

Question 2.

Find:

- 9
^{\(\frac{3}{2}\)} - 32
^{\(\frac{1}{5}\)} - 16
^{\(\frac{3}{4}\)} - 125
^{\(\frac{-1}{3}\)}

Solution:

- 9
^{\(\frac{3}{2}\)}= (3^{2})^{\(\frac{3}{2}\) } - 32
^{\(\frac{2}{2}\)}= (2^{5})^{\(\frac{2}{5}\)} - 16
^{\(\frac{3}{4}\)}= (2^{4})^{\(\frac{3}{4}\)}= (2)^{4x\(\frac{3}{4}\)}= (2)^{3}= 8 - 125
^{\(\frac{1}{3}\)}= (5^{3})^{\(\frac{-1}{3}\)}= (5)^{3x\(\frac{-1}{3}\)}= (5)^{-1}= \(\frac{3}{2}\)

Question 3.

Simplify:

Solution: