Question

a) { [(-4)²]³×(-4)⁵} : (-4)⁹
b(|-2|×(-2)²×|-8|×(-2)⁴
c) [(-2)³×(-2)²]³:(-512)
Urgent! Dau coroana!​

Answer 1

a) { [(-4)²]³×(-4)⁵} : (-4)⁹

$\frac{\left(\left(-4\right)^2\right)^3\left(-4\right)^5}{\left(-4\right)^9}=16$

$\left(\left(-4\right)^2\right)^3\left(-4\right)^5=-4^5\times \left(4^2\right)^3$

$\left(\left(-4\right)^2\right)^3=\left(4^2\right)^3$

$\left(-4\right)^5\left(4^2\right)^3$

$\left(-4\right)^5=-4^5$

$=-\left(4^2\right)^3\times \:4^5$

$=\frac{-4^5\left(4^2\right)^3}{\left(-4\right)^9}$

$\left(-4\right)^9=-4^9$

$=\frac{-4^5\left(4^2\right)^3}{-4^9}$

$=\frac{\left(4^2\right)^3\times \:4^5}{4^9}$

$=\frac{\left(4^2\right)^3}{4^{9-5}}$

$=\frac{\left(4^2\right)^3}{4^4}$

$\left(4^2\right)^3=4^6$

$=\frac{4^6}{4^4}$

$=4^{6-4}$

$=4^2$

$=16$

b) (|-2|×(-2)²×|-8|×(-2)⁴

$\left|-2\right|\left(-2\right)^2\left|-8\right|\left(-2\right)^4$

$=\left|-2\right|\left(-2\right)^{2+4}\left|-8\right|$

$=\left|-2\right|\left(-2\right)^6\left|-8\right|$

$\left(-2\right)^6=64$

$=\left|-2\right|\times \:64\left|-8\right|$

$=2\times \:64\left|-8\right|$

$=2\times \:64\times \:8 = 1024$

c)  [(-2)³×(-2)²]³:(-512)

$\left[\left(-2\right)^3\times \left(-2\right)^2\right]^3\div \left(-512\right)$

$\left(-2\right)^3\times \left(-2\right)^2$

$=-8\times \left(-2\right)^2 =-8\times \:4 =-32$

$=\left(-32\right)^3\div \left(-512\right) =-32768\div \left(-512\right) =64$

Sper că te-am ajutat!

Succes!