Resolver [4^{32}*2^{34}+(2^{5}*2^{20})^{5}:(16*2^23)+(7^5:7^5-1)^32*4]

$$[ 4 ^ { 32 } \cdot 2 ^ { 34 } + ( 2 ^ { 5 } \cdot 2 ^ { 20 } ) ^ { 5 } : ( 16 \cdot 2 ^ { 23 } ) + ( 7 ^ { 5 } : 7 ^ { 5 } - 1 ) ^ { 32 } \cdot 4 ]$$

Avaliar

$$633825300114114700748351602688$$

Passos Para a Resolução

Para multiplicar as potências da mesma base, some os seus expoentes. Some 5 e 20 para obter 25.

$$4^{32}\times 2^{34}+\frac{\left(2^{25}\right)^{5}}{16\times 2^{23}}+\left(\frac{7^{5}}{7^{5}}-1\right)^{32}\times 4$$

Para aumentar uma potência para outra potência, multiplique os expoentes. Multiplique 25 e 5 para obter 125.

$$4^{32}\times 2^{34}+\frac{2^{125}}{16\times 2^{23}}+\left(\frac{7^{5}}{7^{5}}-1\right)^{32}\times 4$$

Dividir 7^{5} por 7^{5} para obter 1.

$$4^{32}\times 2^{34}+\frac{2^{125}}{16\times 2^{23}}+\left(1-1\right)^{32}\times 4$$

Calcule 4 elevado a 32 e obtenha 18446744073709551616.

$$18446744073709551616\times 2^{34}+\frac{2^{125}}{16\times 2^{23}}+\left(1-1\right)^{32}\times 4$$

Calcule 2 elevado a 34 e obtenha 17179869184.

$$18446744073709551616\times 17179869184+\frac{2^{125}}{16\times 2^{23}}+\left(1-1\right)^{32}\times 4$$

Multiplique 18446744073709551616 e 17179869184 para obter 316912650057057350374175801344.

$$316912650057057350374175801344+\frac{2^{125}}{16\times 2^{23}}+\left(1-1\right)^{32}\times 4$$

Anule 2^{23} no numerador e no denominador.

$$316912650057057350374175801344+\frac{2^{102}}{16}+\left(1-1\right)^{32}\times 4$$

Calcule 2 elevado a 102 e obtenha 5070602400912917605986812821504.

$$316912650057057350374175801344+\frac{5070602400912917605986812821504}{16}+\left(1-1\right)^{32}\times 4$$

Dividir 5070602400912917605986812821504 por 16 para obter 316912650057057350374175801344.

$$316912650057057350374175801344+316912650057057350374175801344+\left(1-1\right)^{32}\times 4$$

Some 316912650057057350374175801344 e 316912650057057350374175801344 para obter 633825300114114700748351602688.

$$633825300114114700748351602688+\left(1-1\right)^{32}\times 4$$

Subtraia 1 de 1 para obter 0.

$$633825300114114700748351602688+0^{32}\times 4$$

Calcule 0 elevado a 32 e obtenha 0.

$$633825300114114700748351602688+0\times 4$$

Multiplique 0 e 4 para obter 0.

$$633825300114114700748351602688+0$$

Some 633825300114114700748351602688 e 0 para obter 633825300114114700748351602688.

$$633825300114114700748351602688$$

Fatorizar

$$2^{99}$$