1.

Simplify and express the result in power notation with positive exponent. (i) `(-4)^5 -: (-4)^8` (ii) `(1/(2^3))^2` (iii) `(-3)^4 xx (5/3)^4` (iv) `(3^(-7) -: 3^(-10)) xx 3^(-5)` (v) `2^(-3) xx (-7)^(-3)`

Answer» (i) `(-4 ) -: (-4)^8`
`(-4)^(5-8)`
`(-4)^-3`
`= 1/-4^3`
(ii) `(1/2^3)^2`
`= (2^-3)^2 = 2^-6`
`= 1/2^6`
(iii) `(-3)^4 xx (5/3)^4`
`= (-1)^4*(3)^(4-4)* 5^4`
`= 5^4`
(iv) `(3^-7 -: 3^-10) xx 3^-5`
`= 3^(-7 + 10) xx 3^-5 `
`= 3^3 xx 3^-5`
`= 3^(-5+3) = 3^-2`
`= 1/3^2`
(v) `2^-3 xx (-7)^-3`
`(2 xx -7)^-3= -14^-3`
`1/14^3`
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