Question

Simplifique as expressões aplicando as propriedades das potências.

a)4^1÷3×4^1÷2×4^1÷6=

b)(4^1÷3:2^4÷3)^3÷2=

Ajudem Pf!!!!!

Answer 1

a)

$4^1\div3\times4^1\div2\times4^1\div6~=\\\\\\=~4\div3\times4\div2\times4\div6\\\\\\=~\frac{4}{3}\times4\div2\times4\div6\\\\\\=~\frac{4~.~4}{3}\div2\times4\div6\\\\\\=~\frac{4~.~4}{3~.~2}\times4\div6\\\\\\=~\frac{4~.~4~.~4}{3~.~2}\div6\\\\\\=~\frac{4~.~4~.~4}{3~.~2~.~6}\\\\\\=~\frac{64}{36}\\\\\\Simplificando~por~4\\\\\\=~\boxed{\frac{16}{9}}$

b)

$\left(4^1\div3\div2^4\div3\right)^3\div2~=\\\\\\=~\left(4\div3\div16\div3\right)^3\div2\\\\\\=~\left(\frac{4}{3}\div16\div3\right)^3\div2\\\\\\=~\left(\frac{4}{3~.~16}\div3\right)^3\div2\\\\\\=~\left(\frac{4}{3~.~16~.~3}\right)^3\div2\\\\\\=~\left(\frac{4}{144}\right)^3\div2\\\\\\=~\left(\frac{1}{36}\right)^3\div2\\\\\\=~\left(\frac{1^3}{36^3}\right)\div2\\\\\\=~\frac{1}{46656}\div2\\\\\\=~\frac{1}{46656~.~2}\\\\\\=~\boxed{\frac{1}{93312}}$