Question

simplifique as questões.​

Answer 1

Explicação passo-a-passo:

$a)$  $\frac{9^{2}.27^{3}}{243^{2}}$

    fatorando o 9, 27 e 243, fica

         9 = 3²

         27 = 3³

         243 = 3⁵

    substituindo

         $\frac{(3^{2})^{2}.(3^{3})^{3}}{(3^{5})^{2}}=\frac{3^{2.2}.3^{3}^{3}}{3^{5.2}}=\frac{3^{4}.3^{9}}{3^{10}}=\frac{3^{4+9}}{3^{10}}=\frac{3^{13}}{3^{10}}=3^{13-10}=3^{3}=27$

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$b)$  $\frac{1024.2^{3^{2}}}{64^{3}.8}$

    fatorando o 1024, 64 e 8 e desenvolvendo o $2^{3^{2}}$, fica

         1024 = 2¹⁰

         64 = 2⁶

         8 = 2³

         $2^{3^{2}}$ = 2³ˣ³ = 2⁹

    substituindo

         $\frac{2^{10}.2^{9}}{(2^{6})^{3}.2^{3}}=\frac{2^{10+9}}{2^{6.3}.2^{3}}=\frac{2^{19}}{2^{18}.2^{3}}=\frac{2^{19}}{2^{18+3}}=\frac{2^{19}}{2^{21}}=2^{19-21}=2^{-2}=\frac{1}{2^{2}}=\frac{1}{4}$

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$c)$  $\frac{81^{-5}}{9^{-11}}$

    fatorando o 81 e o 9, fica

         81 = 3⁴

         9 = 3²

    substituindo

         $\frac{(3^{4})^{-5}}{(3^{2})^{-11}}=\frac{3^{4.(-5)}}{3^{2.(-11)}}=\frac{3^{-20}}{3^{-22}}=3^{-20-(-22)}=3^{-20+22}=3^{2}=9$

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$d)$  $[(0,0001)^{3}.100^{4}]^{2}:(0,1)^{7}$

    converta as bases para 10 e fatore o 100

         0,0001 = 10⁻⁴

         100 = 10²

         0,1 = 10⁻¹

    substitua

         [(10⁻⁴)³ · (10²)⁴]² ÷ (10⁻¹)⁷

         [10⁻⁴ˣ³ · 10²ˣ⁴]² ÷ 10⁻¹ˣ⁷

         [10⁻¹² · 10⁸]² ÷ 10⁻⁷

         [10⁻¹²⁺⁸]² ÷ 10⁻⁷

         [10⁻⁴]² ÷ 10⁻⁷

         10⁻⁴ˣ² ÷ 10⁻⁷

         10⁻⁸ ÷ 10⁻⁷ = 10⁻⁸⁻⁽⁻⁷⁾ = 10⁻⁸⁺⁷ = 10⁻¹ = 0,1