Question

Potenciacion algebratica.
Reduce las siguientes expresiones lo mas posible.

Answer 1

1)

${[ \frac{4 {a}^{3} {b}^{4} {c}^{5} }{4 {a}^{2} {b}^{4} c} ]}^{2} = {[1 {a}^{3 - 2} . {b}^{4 - 4}. {c}^{5 - 1} ]}^{2}$

$= {[a. {b}^{0}. {c}^{4} ]}^{2} = {[a {c}^{4} ]}^{2} = {a}^{2} {c}^{8}$

2)

${[ {m}^{3} {n}^{ - 2} {p}^{3} ]}^{ - 1} [ {m}^{5} {n}^{4} {p}^{2} ]$

$( {m}^{ - 3} {n}^{2} {p}^{ - 3} )( {m}^{5} {n}^{4} {p}^{2} )$

$= {m}^{ - 3 + 5} . {n}^{2 + 4} . {p}^{ - 3 + 2}$

$= {m}^{2} {n}^{6} p$

3)

${[ \frac{ {x}^{4} {y}^{ - 3} {z}^{2} }{ {x}^{ - 3} {y}^{2} {z}^{4} } ]}^{ - 3} = [ {x}^{ - 3(4 - ( - 3))} {y}^{ - 3(- 3 - 2)} {z}^{ - 3(2 - 4)} ]$

$= {x}^{ - 3(7)} . {y}^{ - 3( - 5)} . {z}^{ - 3( - 2)}$

$= {x}^{ - 21} {y}^{ 10} {z}^{6}$

$= \frac{ {y}^{10} {z}^{6} }{ {x}^{21} }$