Question

Resuelve y explica las propiedades de la multiplicación y de la potenciación que usaste en cada ejercicio.

35• (2 • 9)2• (22)4• 32 (3 • 9)2 • 93

Answer 1

Verified answer

Respuesta:

= 5.763207191...

Explicación paso a paso:

[tex]35\cdot \:\left(2\:\cdot 9\right)^2\cdot \:\left(22\right)^4\cdot \:32\:\left(3\:\cdot \:9\right)^2\cdot \:93\\\\=22^4\cdot \:35\cdot \:32\cdot \:93\left(2\cdot \:9\cdot \:3\cdot \:9\right)^2\\=22^4\cdot \:486^2\cdot \:35\cdot \:32\cdot \:93\\=35\left(2\cdot \:243\right)^2\cdot \:22^4\cdot \:32\cdot \:93\\=35\cdot \:2^2\cdot \:243^2\cdot \:22^4\cdot \:32\cdot \:93\\=35\cdot \:2^2\cdot \:243^2\left(2\cdot \:11\right)^4\cdot \:32\cdot \:93\\[/tex]

[tex]=35\cdot \:2^2\cdot \:243^2\cdot \:2^4\cdot \:11^4\cdot \:32\cdot \:93\\=35\cdot \:2^2\cdot \:243^2\cdot \:2^4\cdot \:11^4\cdot \:2^5\cdot \:93\\=35\cdot \:243^2\cdot \:11^4\cdot \:2^{2+4+5}\cdot \:93\\=35\cdot \:243^2\cdot \:11^4\cdot \:2^{11}\cdot \:93\\=2^{11}\cdot \:11^4\cdot \:243^2\cdot \:3255\\=2^{11}\cdot \:11^4\cdot \:3255\cdot \:59049\\=2^{11}\cdot \:3255\cdot \:59049\cdot \:14641\\=3255\cdot \:59049\cdot \:14641\cdot \:2048\\=5.763207191...[/tex]