Find the value of:

(a) 7⁰

(b) 7⁷ ÷ 7⁷

(c) (–7)^{2 × 7 – 6 – 8}

(d) (2⁰ + 3⁰ + 4⁰) (4⁰ – 3⁰ – 2⁰)

(e) 2 × 3 × 4 ÷ 2⁰ × 3⁰ × 4⁰

(f) (8⁰ – 2⁰) × (8⁰ + 2⁰)

(a) We have the law of Indices as follows:

a⁰ = 1

Where a = any integer

7⁰ = 1

(b) According to Law of indices,

a^x ÷ a^y = a ^{(x - y)}

Here in the question,

a = 7

x = 7

y = 7

∴ x - y = 7 - 7

= 0

7⁷ ÷ 7⁷ = 7⁰ = 1

(c) (–7)^{2 × 7 – 6 – 8} = (–7)^14-14

= (–7)⁰

= 1

(d) (2⁰ + 3⁰ + 4⁰) (4⁰ – 3⁰ – 2⁰) = (1 + 1 + 1) × (1-1-1)

= 3 × -1

= -3

(e) Let us evaluate the terms separately,

2 × 3 × 4 = 6 × 4

= 24

2⁰ × 3⁰ × 4⁰ = 1 × 1 × 1

= 1

2 × 3 × 4 ÷ 2⁰ × 3⁰ × 4⁰ = 24 / 1

= 24

(f) (8⁰ – 2⁰) × (8⁰ + 2⁰) = (1 – 1) × (1 + 1)

= 0 × 1

= 0