Zgjidh left(111111111^2right)^left(2^2right)^2

$${ \left( { 111111111 }^{ 2 } \right) }^{ { \left( { 2 }^{ 2 } \right) }^{ 2 } }$$

Vlerëso

$$291232396556189435074567831329386972450954523916340519866486047150669094960561024224940246109135493344764854211953905685734600950011383201127797747378082966723304161612131777338064134517583475781525546060624290650872819904629806237902464989778647628372837121$$

Hapat e zgjidhjes

Për të ngritur një fuqi në një fuqi tjetër, shumëzo eksponentët. Shumëzo 2 me 2 për të marrë 4.

$$\left(111111111^{2}\right)^{2^{4}}$$

Llogarit 111111111 në fuqi të 2 dhe merr 12345678987654321.

$$12345678987654321^{2^{4}}$$

Llogarit 2 në fuqi të 4 dhe merr 16.

$$12345678987654321^{16}$$

Llogarit 12345678987654321 në fuqi të 16 dhe merr 291232396556189435074567831329386972450954523916340519866486047150669094960561024224940246109135493344764854211953905685734600950011383201127797747378082966723304161612131777338064134517583475781525546060624290650872819904629806237902464989778647628372837121.

$$291232396556189435074567831329386972450954523916340519866486047150669094960561024224940246109135493344764854211953905685734600950011383201127797747378082966723304161612131777338064134517583475781525546060624290650872819904629806237902464989778647628372837121$$

Faktorizo

$$3^{64}\times 37^{32}\times 333667^{32}$$