Question

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 1

(i) (3⁻⁷ ÷ 3⁻¹⁰) × 3⁻⁵ 

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

= 33 × 3⁻⁵

= 3_{3 + (− 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 ]