Question

Simplify the following:

(i) {(3²)³ x 3⁴} ÷ 3⁷

(ii) 16⁴ ÷ 4²

(iii) \(\frac{5^7}{5^4 \times 5^3}\)

(iv) 4° x 5° x 6°

(v) \(\frac{3^9 \times a^6}{9^2 \times a^3}\)

(vi) (7³ x 7)³

(vii) \(\frac{3^{10}}{3^5 \times 3^7}\)

(viii) \(\frac{a^9}{a^6}\)

(ix) 2° + 3° + 4°

Answer 1

(i) {(3²)³ x 3⁴ } ÷ 3⁷

= {(3)^2×3x 3⁴ ÷ 3⁷ = {(3)⁶ x 3⁴ ) ÷ 3⁷

= (3)⁶⁺⁴ ÷ (3)⁷

= (3)¹⁰ ÷ (3)⁷

= 3^10-7 = 3³

(ii) 16⁴ ÷ 4²

= (4 x 4)⁴ ÷ 4²

= (4¹⁺¹)⁴ ÷ (4)²

= (4)⁸ ÷ (4)² = (4)^8-2 = (4)⁶

(iv) 4° x 5° x 6°

= (4)° x (5)° x (6)°

= 1 x 1 x 1

= 1 {(a)° = 1}

(vi) (7³ x 7)³

= {(7)³⁺¹}³ 

= (7⁴)³ 

= (7)^{4 x 3}

= 7¹²

(ix) 2° + 3° + 4°

= (2)° + (3)° + (4)° 

= 1 + 1 + 1 

= 3