Question

Simplifique.
a) (7²)³
_________________
(7³)²


b) (3.5²)³
_________________
(3².5)²


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Answer 1

Ao simplificarmos,vamos obter A)1 e B)$\large\red{ \sf \dfrac{625}{3}}$

Fazemos Os Cálculos:

A)

$\Large{\text{ \sf \dfrac{\left(7^{2}\right)^{3}}{\left(7^{3}\right)^{2}} }}$

   $\red{\Bigg\downarrow}$

$\Large{\text{ \sf \dfrac{7^{2\times3}}{7^{3\times2}}=\dfrac{7^{6}}{7^{6}}= }}$

$\large\green{\begin{array}{l} \rm Observe\:as\:frac_{\!\!,}\tilde{o}es\:s\tilde{a}o\:as\:mesmas\:no\:resultado\\\rm,ou\:seja, dividimos\:por\:ela\:mesma. \end{array}}$

$\Large\red{\text{ \sf\dfrac{7^{6}}{7^{6}}=1 }}$

$\bf\large{\underline{\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

B)

$\Large{\text{ \sf \dfrac{\left(3\cdot5^{2}\right)^{3}}{\left(3^{2}\cdot5\right)^{2}} }}$

      $\purple{\Bigg\downarrow}$

$\Large\red{\text{ \sf \dfrac{27\times5^{6} }{{3^{4}\times25 }}=\dfrac{3^{3}\times5^{6}}{3^{4}\times5^{2}} }}$

$\Large{\text{ \sf \dfrac{\diagup\!\!\!\!\!3^{3}\times5^{\diagup\!\!\!\!6}}{3^{\diagup\!\!\!\!\!4}\times\diagup\!\!\!\!\!5^{2}} }}$

     $\purple{\Bigg\downarrow}$

   $\Large{\text{ \sf \dfrac{5^{4}}{3}=\dfrac{625}{3} }}$

$\bf\large{\underline{\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$☁

$\Large{\text{\bf Bons~estudos}}$

$\bf\large{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

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