Simplify and express each of the following in exponential form : (i) (2^3 x 3^4 x 4)/(3 x 32)

Question

Simplify and express each of the following in exponential form :

(i) \(\frac{2^3\times3^4\times4}{3\times 32}\)

(ii) ((5²)³ × 5⁴) ÷ 5⁷

(iii) 25⁴ ÷ 5³

^(iv) \(\frac{3\times7^2\times11^8}{21\times 11^3}\)

(v) 2⁰ + 3⁰ + 4⁰

(vi) 2⁰ × 3⁰ × 4⁰

Answer 1

(i) \(\frac{2^3\times3^4\times4}{3\times 32}\)

(ii) ((5²)³ × 5⁴) ÷ 5⁷

= (5^{2 × 3} × 5⁴) ÷ 5⁷ ((a^m)ⁿ = a^mn)

= 5⁶ × 5⁴ ÷ 5⁷

= 5^{6 + 4} ÷ 5⁷ = 5^{10 - 7} = 5³

(iii) 25⁴ ÷ 5³

= (5²)⁴ ÷ 5³ = 5^{2 × 4} ÷ 5³

= 5⁸ ÷ 5³ = 5^{8 - 3} = 5⁵ [a^m ÷ aⁿ = a^{m - n}]

^(iv) \(\frac{3\times7^2\times11^8}{21\times 11^3}\)

= 7^{2 - 1} × 11^{8 – 3} [a^m ÷ aⁿ = a^{m - n}]

= 7¹ × 11⁵ = 7 × 11⁵

(v) 2⁰ + 3⁰ + 4⁰

= 1 + 1 + 1 = [3] [a⁰ = 1]

(vi) 2⁰ × 3⁰ × 4⁰

= 1 × 1 × 1 = 1