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

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

Question 1.
find:

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

Solution:

1. 64^{\(\frac{1}{2}\)} = (8²)^{\(\frac{1}{2}\)}
   
2. 32^{\(\frac{1}{5}\)} = (2⁵)^{\(\frac{1}{5}\)}
   
3. 125^{\(\frac{1}{3}\)} =(5)^{3x\(\frac{1}{2}\)} = 5

Question 2.
Find:

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

Solution:

1. 9^{\(\frac{3}{2}\)} = (3²)^{\(\frac{3}{2}\)}
   
2. 32^{\(\frac{2}{2}\)} = (2⁵)^{\(\frac{2}{5}\)}
3. 16^{\(\frac{3}{4}\)} = (2⁴)^{\(\frac{3}{4}\)} = (2)^{4x\(\frac{3}{4}\)} = (2)³ = 8
4. 125^{\(\frac{1}{3}\)} = (5³)^{\(\frac{-1}{3}\)} = (5) ^{3x\(\frac{-1}{3}\)} = (5)^-1 = \(\frac{3}{2}\)

Question 3.
Simplify:

Solution:

MP Board Class 9th Maths Solutions