Solve z^{33}:[4^{32}*2^{34}+(2^{5}*2^{20})^{5}:(16*2^25)+(7^5:7^5-1)^32*4]

$$z ^ { 33 } : [ 4 ^ { 32 } \cdot 2 ^ { 34 } + ( 2 ^ { 5 } \cdot 2 ^ { 20 } ) ^ { 5 } : ( 16 \cdot 2 ^ { 25 } ) + ( 7 ^ { 5 } : 7 ^ { 5 } - 1 ) ^ { 32 } \cdot 4 ]$$

Evaluate

$$\frac{z^{33}}{396140812571321687967719751680}$$

Solution Steps

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

$$\frac{z^{33}}{4^{32}\times 2^{34}+\frac{\left(2^{25}\right)^{5}}{16\times 2^{25}}+\left(\frac{7^{5}}{7^{5}}-1\right)^{32}\times 4}$$

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

$$\frac{z^{33}}{4^{32}\times 2^{34}+\frac{2^{125}}{16\times 2^{25}}+\left(\frac{7^{5}}{7^{5}}-1\right)^{32}\times 4}$$

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

$$\frac{z^{33}}{4^{32}\times 2^{34}+\frac{2^{125}}{16\times 2^{25}}+\left(1-1\right)^{32}\times 4}$$

Calculate 4 to the power of 32 and get 18446744073709551616.

$$\frac{z^{33}}{18446744073709551616\times 2^{34}+\frac{2^{125}}{16\times 2^{25}}+\left(1-1\right)^{32}\times 4}$$

Calculate 2 to the power of 34 and get 17179869184.

$$\frac{z^{33}}{18446744073709551616\times 17179869184+\frac{2^{125}}{16\times 2^{25}}+\left(1-1\right)^{32}\times 4}$$

Multiply 18446744073709551616 and 17179869184 to get 316912650057057350374175801344.

$$\frac{z^{33}}{316912650057057350374175801344+\frac{2^{125}}{16\times 2^{25}}+\left(1-1\right)^{32}\times 4}$$

Cancel out 2^{25} in both numerator and denominator.

$$\frac{z^{33}}{316912650057057350374175801344+\frac{2^{100}}{16}+\left(1-1\right)^{32}\times 4}$$

Calculate 2 to the power of 100 and get 1267650600228229401496703205376.

$$\frac{z^{33}}{316912650057057350374175801344+\frac{1267650600228229401496703205376}{16}+\left(1-1\right)^{32}\times 4}$$

Divide 1267650600228229401496703205376 by 16 to get 79228162514264337593543950336.

$$\frac{z^{33}}{316912650057057350374175801344+79228162514264337593543950336+\left(1-1\right)^{32}\times 4}$$

Add 316912650057057350374175801344 and 79228162514264337593543950336 to get 396140812571321687967719751680.

$$\frac{z^{33}}{396140812571321687967719751680+\left(1-1\right)^{32}\times 4}$$

Subtract 1 from 1 to get 0.

$$\frac{z^{33}}{396140812571321687967719751680+0^{32}\times 4}$$

Calculate 0 to the power of 32 and get 0.

$$\frac{z^{33}}{396140812571321687967719751680+0\times 4}$$

Multiply 0 and 4 to get 0.

$$\frac{z^{33}}{396140812571321687967719751680+0}$$

Add 396140812571321687967719751680 and 0 to get 396140812571321687967719751680.

$$\frac{z^{33}}{396140812571321687967719751680}$$

Expand

$$\frac{z^{33}}{396140812571321687967719751680}$$

Solution Steps

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

$$\frac{z^{33}}{4^{32}\times 2^{34}+\frac{\left(2^{25}\right)^{5}}{16\times 2^{25}}+\left(\frac{7^{5}}{7^{5}}-1\right)^{32}\times 4}$$

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

$$\frac{z^{33}}{4^{32}\times 2^{34}+\frac{2^{125}}{16\times 2^{25}}+\left(\frac{7^{5}}{7^{5}}-1\right)^{32}\times 4}$$

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

$$\frac{z^{33}}{4^{32}\times 2^{34}+\frac{2^{125}}{16\times 2^{25}}+\left(1-1\right)^{32}\times 4}$$

Calculate 4 to the power of 32 and get 18446744073709551616.

$$\frac{z^{33}}{18446744073709551616\times 2^{34}+\frac{2^{125}}{16\times 2^{25}}+\left(1-1\right)^{32}\times 4}$$

Calculate 2 to the power of 34 and get 17179869184.

$$\frac{z^{33}}{18446744073709551616\times 17179869184+\frac{2^{125}}{16\times 2^{25}}+\left(1-1\right)^{32}\times 4}$$

Multiply 18446744073709551616 and 17179869184 to get 316912650057057350374175801344.

$$\frac{z^{33}}{316912650057057350374175801344+\frac{2^{125}}{16\times 2^{25}}+\left(1-1\right)^{32}\times 4}$$

Cancel out 2^{25} in both numerator and denominator.

$$\frac{z^{33}}{316912650057057350374175801344+\frac{2^{100}}{16}+\left(1-1\right)^{32}\times 4}$$

Calculate 2 to the power of 100 and get 1267650600228229401496703205376.

$$\frac{z^{33}}{316912650057057350374175801344+\frac{1267650600228229401496703205376}{16}+\left(1-1\right)^{32}\times 4}$$

Divide 1267650600228229401496703205376 by 16 to get 79228162514264337593543950336.

$$\frac{z^{33}}{316912650057057350374175801344+79228162514264337593543950336+\left(1-1\right)^{32}\times 4}$$

Add 316912650057057350374175801344 and 79228162514264337593543950336 to get 396140812571321687967719751680.

$$\frac{z^{33}}{396140812571321687967719751680+\left(1-1\right)^{32}\times 4}$$

Subtract 1 from 1 to get 0.

$$\frac{z^{33}}{396140812571321687967719751680+0^{32}\times 4}$$

Calculate 0 to the power of 32 and get 0.

$$\frac{z^{33}}{396140812571321687967719751680+0\times 4}$$

Multiply 0 and 4 to get 0.

$$\frac{z^{33}}{396140812571321687967719751680+0}$$

Add 396140812571321687967719751680 and 0 to get 396140812571321687967719751680.

$$\frac{z^{33}}{396140812571321687967719751680}$$