Simplify and express the result in power notation with positive expone

1.	Simplify and express the result in power notation with positive exponent.(i) ( 3-7 ÷ 3-10 ) x 3-5(ii) 2-3 x (-7)-3
Answer» (i) (3⁻⁷ ÷ 3⁻¹⁰) × 3⁻⁵ = (3⁻⁷ ^{− (−10)}) × 3⁻⁵ (a^m ÷ aⁿ = a^{m − n}) = 33 × 3⁻⁵ = 3₃ _{+ (− 5)} (a_m × a_n = a_{m + n}) = 3−2 = 1/3² ( a^-m = 1/a^m ) (ii) 2⁻³ × (−7)⁻³ = 1/2³ x 1/(-7)³ = 1/[ 2 x (-7) ]³ ( a^-m = 1/a^m ) = 1/(-14)³ [ a^m x b^m= (ab)^m ]

Simplify and express the result in power notation with positive exponent.(i) ( 3-7 ÷ 3-10 ) x 3-5(ii) 2-3 x (-7)-3

Answer»

(i) (3⁻⁷ ÷ 3⁻¹⁰) × 3⁻⁵

= (3⁻⁷ ^{− (−10)}) × 3⁻⁵ (a^m ÷ aⁿ = a^{m − n})

= 33 × 3⁻⁵

= 3₃ _{+ (− 5)} (a_m × a_n = a_{m + n})

= 3−2

= 1/3² ( a^-m = 1/a^m )

(ii) 2⁻³ × (−7)⁻³ = 1/2³ x 1/(-7)³

= 1/[ 2 x (-7) ]³ ( a^-m = 1/a^m )

= 1/(-14)³ [ a^m x b^m= (ab)^m ]