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

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

Evaluate

$$633825300114114700748351602688$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 20 to get 25.

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

To raise a power to another power, multiply the exponents. Multiply 25 and 5 to get 125.

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

Divide 7^{5} by 7^{5} to get 1.

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

Calculate 4 to the power of 32 and get 18446744073709551616.

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

Calculate 2 to the power of 34 and get 17179869184.

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

Multiply 18446744073709551616 and 17179869184 to get 316912650057057350374175801344.

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

Cancel out 2^{23} in both numerator and denominator.

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

Calculate 2 to the power of 102 and get 5070602400912917605986812821504.

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

Divide 5070602400912917605986812821504 by 16 to get 316912650057057350374175801344.

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

Add 316912650057057350374175801344 and 316912650057057350374175801344 to get 633825300114114700748351602688.

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

Subtract 1 from 1 to get 0.

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

Calculate 0 to the power of 32 and get 0.

$$633825300114114700748351602688+0\times 4$$

Multiply 0 and 4 to get 0.

$$633825300114114700748351602688+0$$

Add 633825300114114700748351602688 and 0 to get 633825300114114700748351602688.

$$633825300114114700748351602688$$

Factor

$$2^{99}$$