Question

Utilizando as propriedades de potência com expoente natural, reduza a uma única potência e depois calcule.

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Answer 1

Explicação passo-a-passo:

Lembre-se que:

• $\sf a^m\cdot a^n=a^{m+n}$

• $\sf a^m\div a^n=a^{m-n}$

• $\sf (a^m)^n=a^{m\cdot n}$

• $\sf a^n\cdot b^n=(a\cdot b)^n$

• $\sf a^n\div b^n=(a\div b)^n$

a)

$\sf (3^2)^2=3^{2\cdot2}$

$\sf \red{(3^2)^2=3^{4}}$

$\sf (3^2)^2=3\cdot3\cdot3\cdot3$

$\sf (3^2)^2=9\cdot9$

$\sf \red{(3^2)^2=81}$

b)

$\sf 4^{18}\div4^{15}=4^{18-15}$

$\sf \red{4^{18}\div4^{15}=4^{3}}$

$\sf 4^{18}\div4^{15}=4\cdot4\cdot4$

$\sf 4^{18}\div4^{15}=16\cdot4$

$\sf \red{4^{18}\div4^{15}=64}$

c)

$\sf 5^{2}\cdot5^{1}=5^{5+1}$

$\sf \red{5^{2}\cdot5^{1}=5^{3}}$

$\sf 5^{2}\cdot5^{1}=5\cdot5\cdot5$

$\sf 5^{2}\cdot5^{1}=25\cdot5$

$\sf \red{5^{2}\cdot5^{1}=125}$

d)

$\sf 2^2\cdot6^2=(2\cdot6)^2$

$\sf \red{2^2\cdot6^2=12^2}$

$\sf 2^2\cdot6^2=12\cdot12$

$\sf \red{2^2\cdot6^2=144}$

e)

$\sf 70^3\cdot10^3=(70\div10)^3$

$\sf \red{70^3\cdot10^3=7^3}$

$\sf 70^3\cdot10^3=7\cdot7\cdot7$

$\sf 70^3\cdot10^3=49\cdot7$

$\sf \red{70^3\cdot10^3=343}$

f)

$\sf (10^3)^2=10^{3\cdot2}$

$\sf \red{(10^3)^2=10^{6}}$

$\sf (10^3)^2=10\cdot10\cdot10\cdot10\cdot10\cdot10$

$\sf (10^3)^2=100\cdot100\cdot100$

$\sf (10^3)^2=10000\cdot100$

$\sf \red{(10^3)^2=1000000}$

Answer 2

Oie, Td Bom?!

a)

$= (3 {}^{2} ) {}^{2}$

$= 3 {}^{2 \: . \: 2}$

$= 3 {}^{4}$

$= 3 \: . \: 3 \: . \: 3 \: . \: 3$

$= 81$

b)

$= 4 {}^{18} \div 4 {}^{15}$

$= 4 {}^{18 - 15}$

$= 4 {}^{3}$

$= 4 \: . \: 4 \: . \: 4$

$= 64$

c)

$= 5 {}^{2} \: . \: 5 {}^{1}$

$= 5 {}^{2 + 1}$

$= 5 {}^{3}$

$= 5 \: . \: 5 \: . \: 5$

$= 125$

d)

$= 2 {}^{2} \: . \: 6 {}^{2}$

$= (2 \: . \: 6) {}^{2}$

$= 12 {}^{2}$

$= 12 \: . \: 12$

$= 144$

e)

$= 70 {}^{3} \div 10 {}^{3}$

$= (70 \div 10) {}^{3}$

$= 7 {}^{3}$

$= 7 \: . \: 7 \: . \: 7$

$= 343$

f)

$= (10 {}^{3} ) {}^{2}$

$= 10 {}^{3 \: . \: 2}$

$= 10 {}^{6}$

$= 10 \: . \: 10 \: . \: 10 \: . \: 10 \: . \: 10 \: . \: 10$

$= 1000000$

Att. Makaveli1996