Question

SIMPLIFIQUE:

(2^4)^3 . 5^12 =​

Answer 1

Resposta:3.74144419E+50

Explicação passo-a-passo:

Espero ter ajudado

Answer 2

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⠀⠀☞ Nossa potência simplificada é 10¹². ✅  

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➡️⠀Lembremos de algumas propriedades das potências. A primeira delas é:

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$\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\sf (x^n)^m}&\\&&\\&&\\&\orange{\sf = \overbrace{\sf x^n \cdot x^n \cdot ... \cdot  x^n}^{m~vezes}}&\\&&\\&\orange{\sf = \overbrace{\overbrace{\sf x \cdot x ... \cdot x}^{\sf n~vezes} \cdot \overbrace{\sf x \cdot x ... \cdot x}^{\sf n~vezes} \cdot ... \cdot \overbrace{\sf x \cdot x ... \cdot x}^{\sf n~vezes}}^{m~vezes}}&\\&&\\&&\\&\orange{\sf = x^{(n \cdot m)}}&\\&&\\\end{array}}}}}$

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$\LARGE\blue{\sf (2^4)^3 \cdot 5^{12}}$

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$\LARGE\blue{\sf = 2^{4 \cdot 3} \cdot 5^{12}}$

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$\LARGE\blue{\sf = 2^{12} \cdot 5^{12}}$

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➡️⠀A segunda propriedade é:

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$\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\sf x^n \cdot y^n}&\\&&\\&&\\&\orange{\sf = \overbrace{\sf x \cdot x \cdot ... \cdot x}^{n~vezes} \cdot \overbrace{\sf y \cdot y \cdot ... \cdot y}^{n~vezes}}&\\&&\\&\orange{\sf  = \overbrace{\sf xy \cdot xy \cdot ... \cdot xy}^{n~vezes}}&\\&&\\&&\\&\orange{\sf = (xy)^n}&\\&&\\\end{array}}}}}$

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$\LARGE\blue{\sf = (2 \cdot 5)^{12}}$

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$\LARGE\blue{\sf = 10^{12}}$

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⭐ 1 quadrilhão! ✌

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$\LARGE\green{\boxed{\rm~~~\gray{(2^4)^3 \cdot 5^{12}}~\pink{=}~\blue{ 10^{12} }~~~}}$ ✅

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

⠀⠀☀️ Leia mais sobre potenciação e radiciação:

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