Question

01) Aplique as propriedades da Potenciação:
a)3² . 3⁴ =
b)2² . 2³ . 2⁴ . 2⁶ =
c)-23³ . -23⁶ =

d)-13⁷ : -13⁷ =

e)-25⁸ .-25⁵ : -25⁷ =

f)(- 5 )⁹ : (- 5 )⁶ . (- 5 )⁵ . (- 5 )² =

g)( +2³ )⁶ =

h)[(- 3²)⁴]⁵ =

i){[( 2⁸ . 3⁵ . 5⁸)²]³}

02)Aplique as propriedades da potenciação e resolva;

a)17⁹ : 17⁷ =

b) 11² . 11 =

c)-37⁵ : -37³ =

d)( 2³ . 3² . 5⁴ )³ =

03)Desafio! Aplique a propriedade e resolva;

a)( 8 . 2)⁵ =

b)(121 . 11²)³ =

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Answer 1

01) Aplique as propriedades da Potenciação:

a)3² . 3⁴ =

$3² . 3⁴ = {3}^{2 + 4} = {3}^{6}$

b)2² . 2³ . 2⁴ . 2⁶ =

$2² . 2³ . 2⁴ . 2⁶ = {2}^{2 + 3 + 4 + 6} = {2}^{15}$

c)-23³ . -23⁶ =

$-23³ . -23⁶ = { - 23}^{3 + 6} = { - 23}^{9}$

d)-13⁷ : -13⁷ =

$-13⁷ : -13⁷ = { - 13}^{7 - 7} = { - 13}^{0} = 1$

e)-25⁸ .-25⁵ : -25⁷ =

$-25⁸ .-25⁵ : -25⁷ = { - 25}^{8 + 5 - 7} = { - 25}^{6}$

f)(- 5 )⁹ : (- 5 )⁶ . (- 5 )⁵ . (- 5 )² =

$(- 5 )⁹ : (- 5 )⁶ . (- 5 )⁵ . (- 5 )² = {( - 5)}^{9 - 6 + 5 + 2} = {( - 5)}^{10}$

g)( +2³ )⁶ =

$( +2³ )⁶ = {( + 2)}^{3 \times 6} = {( + 2)}^{18}$

h)[(- 3²)⁴]⁵ =

$[(- 3²)⁴]⁵ = [ { ({ - 3})^{2 \times 4} ]}^{5} =[ { (- 3)}^{8 \times 5} ] = {( - 3)}^{40}$

i){[( 2⁸ . 3⁵ . 5⁸)²]³}

${[( 2⁸ . 3⁵ . 5⁸)²]³} = ({2}^{8} \times {3}^{5} \times {5}^{8} )^{2 \times 3} = ({2}^{8} \times {3}^{5} \times {5}^{8} )^{6} =({2}^{8 \times 6} \times {3}^{5 \times 6} \times {5}^{8 \times 6} ) = {2}^{48} \times {3}^{30} \times {5}^{48}$

02)Aplique as propriedades da potenciação e resolva;

a)17⁹ : 17⁷ =

$17⁹ : 17⁷ = {17}^{9 - 7} = {17}^{2} = 289$

b) 11² . 11 =

$11² . 11 = {11}^{2 + 1} = {11}^{3} = 1331$

c)-37⁵ : -37³ =

$-37⁵ : -37³ = { - 37}^{5 - 3} = { - 37}^{2} = 1369$

d)( 2³ . 3² . 5⁴ )³ =

$( 2³ . 3² . 5⁴ )³ = {(8 \times 9 \times 625)}^{3} = {45000}^{3} = 91.125.000.000.000$

03)Desafio! Aplique a propriedade e resolva;

a)( 8 . 2)⁵ =

$( 8 . 2)⁵ = {8}^{5} \times {2}^{5} =32.768 \times32 = 1.048.576 \\ou \\ ( 8 . 2)⁵ = {16}^{5} = 1.048.576$

b)(121 . 11²)³ =

$(121 . 11²)³ = ({ {11}^{2} \times {11}^{2} })^{3} = {( {11}^{4} )}^{3} = {11}^{4 \times 3} = {11}^{12} = 3.138.428.376.721$