Question

1 ) Reduza a uma só potência

 a) 5⁴ : 5² =                            

b) 8⁷ : 8³ =

 c) 9⁵ : 9² =

 d) 4³ : 4² =

 e) 9⁶ : 9³ =

 f) 9⁵ : 9 =

g) (5⁴)²

 h) (7²)⁴

 i) (4³)²

j) 7² . 7⁶ =

 k) 2² . 2⁴=

 l) 5 . 5³ = 

m) 8² . 8 =

​

Answer 1

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EXPLICAÇÃO PASSO-A-PASSO_____✍

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☺lá, Babyshark, como tens passado nestes tempos de quarentena⁉ E os estudos à distância, como vão⁉ Espero que bem❗ Acompanhe a resolução abaixo, feita através de algumas manipulações algébricas, e após o resultado você encontrará um link com mais informações sobre Potenciação e Radiciação que talvez te ajude com exercícios semelhantes no futuro. ✌

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Ⓐ_____________________________✍

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$\Large\gray{\boxed{\rm\blue{ 5^4 \div 5^2 }}}$

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$\large\sf\blue{ = 5^4 \times 5^{-2}}$

$\large\sf\blue{ = 5^{4 + (-2)}}$

$\large\sf\blue{ = 5^{4 - 2}}$

$\large\sf\blue{ = 5^2}$

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$\LARGE\green{\boxed{\rm~~~\red{ A)}~\gray{5^4 \div 5^2}~\pink{=}~\blue{ 5^2  }~~~}}$ ✅

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Ⓑ_____________________________✍

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$\Large\gray{\boxed{\rm\blue{ 8^7 \div 8^3 }}}$

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$\large\sf\blue{ = 8^7 \times 8^{-3}}$

$\large\sf\blue{ = 8^{7 + (-3)}}$

$\large\sf\blue{ = 8^{7 - 3}}$

$\large\sf\blue{ = 8^4}$

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$\LARGE\green{\boxed{\rm~~~\red{ B)}~\gray{8^7 \div 8^3}~\pink{=}~\blue{ 8^4 }~~~}}$ ✅

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Ⓒ_____________________________✍

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$\Large\gray{\boxed{\rm\blue{9^{5} \div 9^{2}}}}$

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$\large\sf\blue{ = 9^{5} \times 9^{-2}}$

$\large\sf\blue{ = 9^{5 + (-2)}}$

$\large\sf\blue{ = 9^{5 - 2}}$

$\large\sf\blue{ = 9^{3}}$

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$\LARGE\green{\boxed{\rm~~~\red{ C)}~\gray{9^{5} \div 9^{2}}~\pink{=}~\blue{ 9^{3} }~~~}}$ ✅

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Ⓓ_____________________________✍

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$\Large\gray{\boxed{\rm\blue{4^{3} \div 4^{2}}}}$

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$\large\sf\blue{ = 4^{3} \times 4^{-2}}$

$\large\sf\blue{ = 4^{3 + (-2)}}$

$\large\sf\blue{ = 4^{3 - 2}}$

$\large\sf\blue{ = 4^{1}}$

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$\LARGE\green{\boxed{\rm~~~\red{ D)}~\gray{4^{3} \div 4^{2}}~\pink{=}~\blue{ 4^{1} }~~~}}$ ✅

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Ⓔ_____________________________✍

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$\Large\gray{\boxed{\rm\blue{9^{6} \div 9^{3}}}}$

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$\large\sf\blue{ = 9^{6} \times 9^{-3}}$

$\large\sf\blue{ = 9^{6 + (-3)}}$

$\large\sf\blue{ = 9^{6 - 3}}$

$\large\sf\blue{ = 9^{3}}$

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$\LARGE\green{\boxed{\rm~~~\red{ E)}~\gray{9^{6} \div 9^{3}}~\pink{=}~\blue{ 9^{3} }~~~}}$ ✅

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Ⓕ_____________________________✍

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$\Large\gray{\boxed{\rm\blue{9^{5} \div 9^{1}}}}$

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$\large\sf\blue{ = 9^{5} \times 9^{-1}}$

$\large\sf\blue{ = 9^{5 + (-1)}}$

$\large\sf\blue{ = 9^{5 - 1}}$

$\large\sf\blue{ = 9^{4}}$

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$\LARGE\green{\boxed{\rm~~~\red{ F)}~\gray{9^{5} \div 9^{1}}~\pink{=}~\blue{ 9^{4} }~~~}}$ ✅

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Ⓖ_____________________________✍

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$\Large\gray{\boxed{\rm\blue{ (5^4)^2 }}}$

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$\large\sf\blue{ = 5^{4 \times 2} }$

$\large\sf\blue{ = 5 ^{8}}$

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$\LARGE\green{\boxed{\rm~~~\red{ G)}~\gray{(5^4)^2}~\pink{=}~\blue{5 ^{8}}~~~}}$ ✅

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Ⓗ_____________________________✍

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$\Large\gray{\boxed{\rm\blue{ (7^2)^4 }}}$

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$\large\sf\blue{ = 7^{2 \times 4} }$

$\large\sf\blue{ = 7 ^{8}}$

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$\LARGE\green{\boxed{\rm~~~\red{ H)}~\gray{(7^2)^4}~\pink{=}~\blue{7 ^{8}}~~~}}$ ✅

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Ⓘ_____________________________✍

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$\Large\gray{\boxed{\rm\blue{ (4^3)^2 }}}$

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$\large\sf\blue{ = 4^{3 \times 2} }$

$\large\sf\blue{ = 4 ^{6}}$

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$\LARGE\green{\boxed{\rm~~~\red{ I)}~\gray{(4^3)^2}~\pink{=}~\blue{4 ^{6}}~~~}}$ ✅

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Ⓙ_____________________________✍

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$\Large\gray{\boxed{\rm\blue{ 7^2 \times 7^6 }}}$

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$\large\sf\blue{ = 7^{2 + 6} }$

$\large\sf\blue{ = 7^{8} }$

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$\LARGE\green{\boxed{\rm~~~\red{ J)}~\gray{7^2 \times 7^6}~\pink{=}~\blue{ 7^{8} }~~~}}$ ✅

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Ⓚ_____________________________✍

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$\Large\gray{\boxed{\rm\blue{ 2^2 \times 2^4 }}}$

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$\large\sf\blue{ = 2^{2 + 4} }$

$\large\sf\blue{ = 2^{6} }$

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$\LARGE\green{\boxed{\rm~~~\red{ K)}~\gray{2^2 \times 2^4}~\pink{=}~\blue{ 2^{6} }~~~}}$ ✅

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Ⓛ_____________________________✍

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$\Large\gray{\boxed{\rm\blue{ 5^1 \times 5^3 }}}$

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$\large\sf\blue{ = 5^{1 + 3} }$

$\large\sf\blue{ = 5^{4} }$

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$\LARGE\green{\boxed{\rm~~~\red{ L)}~\gray{5^1 \times 5^3}~\pink{=}~\blue{ 5^{4} }~~~}}$ ✅

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M)_____________________________✍

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$\Large\gray{\boxed{\rm\blue{ 8^2 \times 8^1 }}}$

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$\large\sf\blue{ = 8^{2 + 1} }$

$\large\sf\blue{ = 8^{3} }$

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$\LARGE\green{\boxed{\rm~~~\red{ M)}~\gray{8^2 \times 8^1}~\pink{=}~\blue{ 8^{3} }~~~}}$ ✅

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Answer 2

Resposta:

Explicação passo-a-passo:

1 ) Reduza a uma só potência

a) 5⁴ : 5² = 5^(4-2)= 5^2

b) 8⁷ : 8³ = 8^(7-3)= 8^4

c) 9⁵ : 9² = 9^(5-2)= 9^3

d) 4³ : 4² =4^(3-2)= 4^1 = 4

e) 9⁶ : 9³ = 9^(6-3)= 9^3

f) 9⁵ : 9 = 9^(5-1)= 9^4

g) (5⁴)² 5^(4.2)= 5^8

h) (7²)⁴ = 7^(2.4)= 7^8

i) (4³)² = 4^(3.2)= 4^6

j) 7² . 7⁶ =7^(2+6)= 7^8

k) 2² . 2⁴= 2^(2+4)= 2^6

l) 5 . 5³ = 5^(1+3)= 5^4

m) 8² . 8 = 8^(2+1)= 8^3