Question

Transforme em produto o quociente de potências:

$[ ( \frac{a}{b} )^{p} . (\frac{a}{b} )^{-p} ] ^{q}$ =



$( \frac{a^{2} }{ a^{3} } )^{-2} . ( \frac{ a^{-5} }{ a^{3} } ) ^{-1} / ( \frac{ a^{4} }{ a^{7} } ) ^{2}$  =

Answer 1

a)
$[( \frac{a}{b} )^p.( \frac{a}{b} )^-^p}]^q=$

$[ \frac{a^p}{b^p} . \frac{b^p}{a^p} ]^q=$

cancela e fica  $\fbox{ 1^q }$

b)

$( \frac{a^2}{a^3} )^-^2.( \frac{a^-^5}{a^3} )^-^1\div(a^-^3)^2=$

$(a^2 \div a^3 )^-^2 \times(a^-^5 \div a^3)^-^1 \div(a^-^3 )^2=$

$(a^-^1)^-^2 .(a^-^8)^-^1 \div a^-^6=$

$a^2 \times a^8 \div a^-^6=$

$a^1^0\div a ^-^6=a^{10+6} = \fbox{ a^{16} }$