What is ((4p^{-4}q)^{-2})/(10pq^{-3)} ?

The solution to ((4p^{-4}q)^{-2})/(10pq^{-3)} is (p^7q)/(160)

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simplify ((4p^{-4}q)^{-2})/(10pq^{-3)}

simplify

\frac{( 4 p ^{- 4} q ) ^{- 2}}{10 p q ^{- 3}}

\frac{p ^{7} q}{160}

Solution steps

\frac{( 4 p ^{- 4} q ) ^{- 2}}{10 p q ^{- 3}}

Simplify

(4 p^{- 4} q)^{- 2} : 4^{- 2} p^{8} q^{- 2}

= \frac{4 ^{- 2} p ^{8} q ^{- 2}}{10 p q ^{- 3}}

Factor

4^{- 2} : 2^{- 4}

= \frac{2 ^{- 4} p ^{8} q ^{- 2}}{10 p q ^{- 3}}

Factor the number:

10 = 2 \cdot 5

= \frac{2 ^{- 4} p ^{8} q ^{- 2}}{2 \cdot 5 p q ^{- 3}}

\frac{2 ^{- 4}}{2} = \frac{1}{2 ^{5}}

= \frac{p ^{8} q ^{- 2}}{2 ^{5} \cdot 5 p q ^{- 3}}

Simplify

\frac{p ^{8}}{p} : p^{7}

= \frac{p ^{7} q ^{- 2}}{2 ^{5} \cdot 5 q ^{- 3}}

Simplify

\frac{q ^{- 2}}{q ^{- 3}} : q

= \frac{p ^{7} q}{2 ^{5} \cdot 5}

2^{5} \cdot 5 = 160

= \frac{p ^{7} q}{160}

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\frac{x ^{2} + 4 x + 3}{x - 1} > 0

9 a^{2} + 12 ab + 4 b^{2}

3 (x - 1) = 2 x + 9

What is ((4p^{-4}q)^{-2})/(10pq^{-3)} ?
The solution to ((4p^{-4}q)^{-2})/(10pq^{-3)} is (p^7q)/(160)