Question

Y= 4¹º.8-³.16-²/32
metade de y vale?

Answer 1

Bom dia.
Resolução.

Y/2=??

Resolvendo o numerador:
4¹⁰ = 4*4*4*4*4*4*4*4*4*4= 1048576
8⁻³ = 1 / 8³ = 8*8*8 = 1/512
16⁻² = 1 / 16² = 1/ 16*16 = 1/256

Y = 1048576 x 1/512 x 1/256 = 1048576 / 131072 = 8
Y = 8/32 (simplificando por 8), temos:
Y = 1/4
Vou dividir 1/4 por 2, e teremos o resultado final.

Y = 1/4 /2 = 1/4 x 1/2 = 1/8

∴ Y/2 = 1/8

Espero ter ajudado.

Answer 2

$Y=\dfrac{4^{10}\cdot 8^{-3}\cdot 16^{-2}}{32}\\ \\ \\ Y=\dfrac{\left(2^{2}\right)^{10}\cdot \left(2^{3}\right)^{-3}\cdot \left(2^4\right)^{-2}}{2^{5}}\\ \\ \\ Y=\dfrac{\left(2^{2\cdot 10}\right)\cdot \left(2^{3\cdot \left(-3\right)}\right)\cdot \left(2^{4\cdot \left(-2\right)}\right)}{2^{5}}\\ \\ \\ Y=\dfrac{2^{20}\cdot 2^{-9}\cdot 2^{-8}}{2^{5}}\\ \\ \\ Y=\dfrac{2^{20+\left(-9\right)+\left(-8\right)}}{2^{5}}\\ \\ \\ Y=\dfrac{2^{20-9-8}}{2^{5}}\\ \\ \\ Y=\dfrac{2^{3}}{2^{5}}$

$Y={2^{3}:2^{5}=2^{3-5}=2^{-2}$

A metade de Y é:

$\dfrac{Y}{2}=\ \dfrac{2^{-2}}{2}=\ 2^{-2}:2=\ 2^{-2-1}=2^{-3}\\ \\ Ou\ \Rightarrow 2^{-3}=\dfrac{1}{2^{3}}=\dfrac{1}{8}$