Simplify and express the result in power notation with positive exponent.


(i) (-4)5 ÷ (-4)8  


(ii) 


(iii) 


(iv) (3-7 ÷ 3-10) × 3-5


(v)  2-3 × (-7)-3


 


 


(i) Formula: am ÷ an = a(m-n)


By using above formula in question:


(-4)5 ÷ (-4)8


= (-4)5-8


= (-4)-3


= 1/(-4)3


= -1/64


 


(ii) Formula: (am)n = amn


By using above formula in question:



 


(iii) Formula:- am ÷ an = a(m-n)



= 54


= 625


 


(iv) Formula:- am ÷ an = a(m-n)


am × an = a{m+n}


By using above formula in question:


(3-7÷ 3-10) × 3-5


= (3 (-7+10)) × 3-5


= 33 × 3-5


= 3 (3-5)


= 3-2


= 1/9


 


(v) 2-3 × (-7)-3


= 1/23 – 1/73


= 1/8 × 1/343


= 1/2744

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