**1. Find:**

**(i)64 ^{1/2}**

**Solution:**

= 64 ^{1/2} = (8×8) ^{1/2}

= (8^{2})^{1/2}

= 8^{1} [2×1/2 = 2/2 =1]

= 8

**(ii)32 ^{1/5}**

**Solution:**

= 32 ^{1/5} = (2^{5})^{1/5}

= (2^{5}) ^{1/5}

= 2^{1} [5×1/5 = 1]

= 2

**(iii)125 ^{1/3}**

**Solution:**

= (125) ^{1/3} = (5×5×5)^{1/3}

= (5^{3})^{1/3}

= 5^{1} (3×1/3 = 3/3 = 1)

= 5

**2. Find:**

**(i) 9 ^{3/2}**

Solution:

=9^{3/2} = (3×3)3/2

= (3^{2})^{3/2}

= 3^{3} [2×3/2 = 3]

=27

**(ii) 32 ^{2/5}**

**Solution:**

=32^{2/5} = (2×2×2×2×2)2/5

= (2^{5})^{2⁄5}

= 2^{2} [5×2/5= 2]

= 4

**(iii)16 ^{3/4}**

**Solution:**

= 16^{3/4} = (2×2×2×2)^{3/4}

= (2^{4})^{3⁄4}

= 2^{3} [4×3/4 = 3]

= 8

**(iv) 125 ^{(-1/3)}**

**Solution:**

= 125 ^{-1/3} = (5×5×5) ^{-1/3}

= (5^{3}) ^{-1⁄3}

= 5-1 [3×-1/3 = -1]

= 1/5

**3. Simplify:**

**(i) 2 ^{2/3} × 2 ^{1/5}**

**Solution:**

= 2 ^{2/3} × 2 ^{1/5} = 2 ^{(2/3)+(1/5)} [a^{m }× a^{n }=a ^{m+n}]

[Here, 2/3 + 1/5 = (2×5+3×1)/(3×5) = 13/15]

= 2^{13/15}

**(ii) (1/3 ^{3})^{7}**

**Solution:**

= (1/3^{3})^{7} = (3 ^{-3})^{7}

= 3 ^{-21}

**(iii) 11 ^{1/2}/11 ^{1/4}**

**Solution:**

= 11 ^{1/2}/11 ^{1/4}

= 11 ^{(1/2)-(1/4)}

[(1/2) – (1/4) = (1×4-2×1)/(2×4) = 4-2)/8 = 2/8 = ¼ ]

= 11 ^{1/4}

**(iv) 7 ^{½} × 8 ^{1/2}**

**Solution:**

7 ^{½} × 8 ^{1/2}

= (7×8) ^{1/2}

= 56 ^{1/2}

**👍👍👍**