Question

usando as propriedades de potência simplifique as expressões da foto ME AJUDEM PFV 15 pontos :(

Answer 1

Resposta:

Explicação passo-a-passo:

a) $[(\frac{1}{1024} )^{-3} *64]*2^{3}$

Aplicar a propriedade do expoente :

$a^{-b}=\frac{1}{a^b}$

$=2^3\cdot \:64\cdot \frac{1}{\left(\frac{1}{1024}\right)^3}$

$\frac{1}{\left(\frac{1}{1024}\right)^3}=1024^3$

$=\left(2^{10}\right)^3\cdot \:64\cdot \:2^3$

$=2^{30}\cdot \:2^6\cdot \:2^3$

$=2^{30+6+3}$

$=2^{39}$

B) $\frac{(\frac{729}{3}) ^{2}}{(\frac{1}{9}) ^{-2} }$

$\left(\frac{1}{9}\right)^{-2} =\frac{1}{\left(\frac{1}{9}\right)^2}$

$=\frac{1}{\frac{1^2}{9^2}}=9^2$

$=\frac{\left(\frac{729}{3}\right)^2}{9^2}=\frac{243^2}{9^2}$

$\mathrm{Fatorar\:}243=3^5$

$=\left(3^5\right)^2=3^{10}$

$\mathrm{Fatorar\:}9=3^2=\left(3^2\right)^2$

$\frac{3^{10}}{3^4}=3^{10-4}$

$3^6=729$