Question

encontrar o menor resultado em formato de potencia:​

Answer 1

Resposta:

a) $1960^{3}$  e b) $\frac{2^{3}.5 }{3^{2} }$

Explicação passo-a-passo:

a)

$5^{3} . 6^{3} .7^{2} .7^{4} .2^{2} .2^{4} =\\\\5^{3} . (2.3)^{3} .7^{2+4} .2^{2+4} =\\5^{3} . 2^3.3^{3} .7^{6} .2^{6} =\\\\5^{3} . 2^3.3^{3} .7^{3+3} .2^{3+3}=\\5^{3} . 2^3.3^{3} .7^{3}.7^{3}.2^{3}.2^{3}=\\(5.2.7.7.2.2)^{3} =\\1960^{3}$

b)$\frac{4^{3}.2^{3} .5 }{2^{2}.3^{2}.4^{2} } =\frac{(2^2)^{3}.2^{3} .5 }{2^{2}.3^{2}.(2^2)^{2} } =\frac{2^{6}.2^{3} .5 }{2^{2}.3^{2}.2^{4} } = \frac{2^{9}.5 }{2^{6}.3^{2} } = \frac{2^{3}.5 }{3^{2} } = \frac{40}{9}$