Question

socorro gente isso vale a nota toda, é pra segunda ​

Answer 1

Explicação passo-a-passo:

1- a) Fatorando o 81 = $3^{4}$

       $3^{4}.81^{2}=3^{4}.(3^{4})^{2}=3^{4}.3^{8}=3^{4+8}=3^{12}$

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   b) Fatorando o 8 = $2^{3}$

       $2^{4}.8=2^{4}.2^{3}=2^{4+3}=2^{7}$

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   c) Fatorando o 25 = $5^{2}$

       $\sqrt{5^{2}}.\sqrt{\sqrt{25^{2}}}=5.\sqrt{25}=5.\sqrt{5^{2}}=5.5=25$

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   d) Fatorando o 8 = $2^{3}$

        $8^{2}*2^{\frac{4}{2}}=(2^{3})^{2}.\sqrt{2^{4}}=2^{6}.2^{2}=2^{8}$

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   e) $\frac{2048^{0}}{1^{-9}}=\frac{1}{1^{-9}}=1^{1-(-9)}=1^{1+9}=1^{10}$

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   f) Fatorando o 64 = $2^{6}$ e 4 = $2^{2}$

      $\frac{64.4^{2}}{2^{-2}}=\frac{2^{6}.(2^{2})^{2}}{2^{-2}}=\frac{2^{6}.2^{4}}{2^{-2}}=\frac{2^{10}}{2^{-2}}=2^{10-(-2)}=2^{10+2}=2^{12}$

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2- a) $x^{2}y.x^{6}.x^{-2}y^{-1}=x^{2+6-2}y^{1-1}=x^{6}y^{0}=x^{6}$

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   b) $\frac{(6x-2x)}{2xb}=\frac{4x}{2xb}=\frac{2}{b}$

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   c) $2xy^{2}.\sqrt{x^{2}y^{2}}.ay.b^{2}=2xy^{2}.xy.ay.b^{2}=2x^{1+1}y^{2+1+1}ab^{2}=2x^{2}y^{4}ab^{2}$

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   d) $9ab^{2}c^{4}.3a^{-1}b^{6}c^{-9}=27a^{1-1}b^{2+6}c^{4-9}=27b^{8}c^{-5}$

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   e) $\frac{81p^{2}r^{6}}{9^{2}pr^{2}}=\frac{81p^{2}r^{6}}{81pr^{2}}=1.p^{2-1}r^{6-2}=pr^{4}$

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   f) $\frac{\sqrt{(-x)^{2}}.6b}{-2axb}=\frac{x.6b}{-2axb}=\frac{-3}{a}=-\frac{3}{a}$