**1. Evaluate:**

**(i) 3 ^{-2} (ii) (-4)^{-2} (iii) (1/2)^{-5} **

**Solution:**

**(i) 3 ^{-2}** = (1/3)

^{2}

[a^{-m} = 1/a^{m}]

= 1/9

**(ii) (-4)**^{-2} = (1/-4)^{2}

[a^{-m} = 1/a^{m}]

= 1/16

**(iii) (1/2)**^{-5} = (2/1)^{5}

[a^{-m} = 1/a^{m}]

= 2^{5}

= 32

**2. Simplify and express the result in power notation with positive exponent:**

**(i)(-4) ^{5} ÷(-4)^{8} **

**Solution:**

= [ a^{m} / a^{n} = a^{m-n}]

= (-4)^{5-8}

= 1/4^{3}

**(ii) (1/2 ^{3})^{2} **

**Solution:**

= 1^{2}/ (2^{3})^{2}

= 1/2^{6}

**(iii) (-3) ^{4}× (5/3)^{4}**

**Solution:**

= (-3)^{4 }× (5^{4}/3^{4})

= 5^{4}

**(iv) (3 ^{-7}÷3^{-10}) ×3^{-5} **

**Solution:**

= 3^{-7 – 10} × 3^{-5}

= 3^{3 } × 3^{-5}

= 3^{-2}

= 1/3^{2 }

**(v) 2 ^{-3 }× (-7)^{-3}**

**Solution:**

= [2× (-7)]^{-3}

= (-14)^{-3}

= -(1/14^{3})

**3. Find the value of:**

**(i)(3 ^{0}+4^{-1})×2^{2}**

**Solution:**

= (1+(1/4)) ×2^{2}

= ((4+1)/4) ×2^{2}

= (5/4) ×4

= 5

**(ii) (2 ^{-1}×4^{-1}) ÷2 ^{– 2}**

**Solution:**

= [(1/2)×(1/4)] ÷(1/4)

= (1/2×1/2^{2}) ÷ 1/4

= 1/2^{3} ÷ 1/4

= (1/8) × (4)

= 1/2

**(iii) (1/2) ^{-2}+(1/3)^{-2}+(1/4)^{-2}**

**Solution:**

= (2^{-1})^{-2}+(3^{-1})^{-2}+(4^{-1})^{-2}

= 2^{(-1×-2)} + 3^{(-1×-2)} + 4^{(-1×-2)}

= 2^{2}+3^{2}+4^{2}

= 4+9+16

=29

**(iv) (3 ^{-1}+4^{-1}+5^{-1})^{0}**

**Solution:**

= 1

**(v) {(-2/3)-2} ^{2}**

**Solution:**

= (-2/3)^{-2×2}

= (-2/3)^{-4}

= (-3/2)^{4}

= 81/16

**4. Evaluate**

(i)(8^{-1}×5^{3})/2^{-4}

(ii) (5^{-1}×2^{-2}) × 6^{-1}

**Solution:**

**5. Find the value of m for which 5 ^{m} ÷ 5^{-3} = 5^{5}**

**Solution:**

Given, 5^{m} ÷ 5^{-3} = 5^{5}

5^{m-(-3) }= 5^{5} [a^{m} ÷ a^{n} = a^{m-n}]

5 ^{m+3} = 5^{5}

Comparing the powers of equal bases

m + 3 = 5

m = 5 – 3 = 2

m = 2

**6.Evaluate:**

**Solution:**

**Solution:**

**7. Simplify:**

**Solution:**

**Given:**

**Solution:**

**👍👍👍**