Question

1) Aplique as propriedades da potenciação:

a) 7¹³/7⁶

b)6-²⁰.6¹⁴.(6³)² / 6‐⁵.6¹²

c)81³.9-² / 27⁴

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Answer 1

Explicação passo-a-passo:

Explicação passo-a-passo:

$a) \frac{7 {}^{13}}{7 {}^{6}}$

$7 {}^{13-6}$

$7 {}^{7} = 7x7x7x7x7x7x7 = 823.543$

Outra forma de resolver:

$\frac{7 {}^{13}}{7 {}^{6}} =$

$\frac{7x7x7x7x7x7x7x7x7x7x7x7x7}{7x7x7x7x7x7} </p><p>= 7x7x7x7x7x7x7 = 823.543 Alternativa B:</p><p>[tex] b) \frac{6 {}^{-20+14}×6 {}^{3×2}}{6 {}^{-5+12}} = \frac{6 {}^{-6}×6 {}^{6}}{6 {}^{-7}} =\frac{6 {}^{-6+6}}{6 {}^{-7}} = \frac{6 {}^{0}}{6 {}^{-7}} = 6 {}^{0-(-7)} = 6 {}^{7} = 6×6×6×6×6×6×6 = 279.936$

Alternativa C:

$\frac{81 {}^{3}×9 {}^{-2}}{27 {}^{4}} = \frac{(3 {}^{4}) {}^{3}×(3 {}^{2}) {}^{-2}}{(3 {}^{3}) {}^{4}} = \frac{3 {}^{4×3}×3 {}^{2×(-2)}}{3 {}^{3×4}} = 3 {}^{-4} = \frac{1}{3 {}^{4}} = \frac{1}{3×3×3×3} = \frac{1}{81}$