Question

Usando as propriedades de potências, escreva na forma de uma só potência: *
me ajudem por favoooorrr!!!​

Answer 1

Resposta:

a) (5)-¹= 1/5

$b) ( \frac{4}{3} ) {}^{ - 2} = ( \frac{3}{4} ) {}^{2} = \frac{3}{4} . \frac{3}{4} = \frac{9}{16}$

$c) \: \: ( - 2) { - }^{2} = ( \frac{1}{2} ) {}^{2} = \frac{1}{2} . \frac{1}{2} = \frac{1}{4}$

$d)8 {}^{7} .8 {}^{2} = 8 {}^{7 + 2} = 8 {}^{9}$

$e) \: \: \frac{6 {}^{5} }{6 {}^{6} } = 6 {}^{5 - 6} = 6 {}^{ - 1} = \frac{1}{6}$

$f) \: \: (10 {}^{5} ) {}^{4} = 10 {}^{5 \times 4} = 10 {}^{20}$

Answer 2

Resposta:

$5^-^1\\\\\mathrm{Aplicar\:as\:propriedades\:dos\:expoentes}:\quad \:a^{-1}=\frac{1}{a}\\\\=\frac{1}{5}$

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$(\frac{4}{3}) ^-^2\\\\\mathrm{Aplicar\:as\:propriedades\:dos\:expoentes}:\quad \:a^{-b}=\frac{1}{a^b}\\\\\left(\frac{4}{3}\right)^{-2}=\frac{1}{\left(\frac{4}{3}\right)^2}\\\\\frac{1}{\left(\frac{4}{3}\right)^2}\\\\\frac{1}{\frac{16}{9}}\\\\=\frac{9}{16}$

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$(-2)^-^2\\\\\mathrm{Aplicar\:as\:propriedades\:dos\:expoentes}:\quad \:a^{-b}=\frac{1}{a^b}\\\\\left(-2\right)^{-2}=\frac{1}{\left(-2\right)^2}\\\\\frac{1}{\left(-2\right)^2}\\\\=\frac{1}{4}$

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$8^7*8^2\\\\\mathrm{Aplicar\:as\:propriedades\:dos\:expoentes}:\quad \:a^b\cdot \:a^c=a^{b+c}\\\\8^{7+2}\\\\8^9=134217728$

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$6^5:6^6\\\\=6^{5-6}\\\\\mathrm{Aplicar\:as\:propriedades\:dos\:expoentes}:\quad \:a^{-1}=\frac{1}{a}\\\\=\frac{1}{6}$

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$(10^5)^4\\\\\left(10^5\right)^4=10^{5\cdot \:4}\\\\=10^{5\cdot \:4}\\\\=10^{20}$