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: a^{m} ÷ a^{n} = 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: (a^{m})^{n} = a^{mn}

By using above formula in question:

(iii) Formula:- a^{m} ÷ a^{n} = a^{(m-n)}

= 5^{4}

= 625

(iv) Formula:- a^{m} ÷ a^{n} = a^{(m-n)}

a^{m} × a^{n} = a^{{m+n}}

By using above formula in question:

(3^{-7}÷ 3^{-10}) × 3^{-5}

= (3 ^{(-7+10)}) × 3^{-5}

= 3^{3} × 3^{-5}

= 3 ^{(3-5)}

= 3^{-2}

= 1/9

(v) 2^{-3} × (-7)^{-3}

= 1/2^{3} – 1/7^{3}

= 1/8 × 1/343

= 1/2744

12