Solve {[(20*5+16div2-3^{3})div3]^{7}div3^5}^4div3^8^2

$$\{ [ ( 20 \cdot 5 + 16 \div 2 - 3 ^ { 3 } ) \div 3 ] ^ { 7 } \div 3 ^ { 5 } \} ^ { 4 } \div 3 ^ { 8 ^ { 2 } }$$

Evaluate

$$1$$

Solution Steps

Multiply 20 and 5 to get 100.

$$\frac{\left(\frac{\left(\frac{100+\frac{16}{2}-3^{3}}{3}\right)^{7}}{3^{5}}\right)^{4}}{3^{8^{2}}}$$

Divide 16 by 2 to get 8.

$$\frac{\left(\frac{\left(\frac{100+8-3^{3}}{3}\right)^{7}}{3^{5}}\right)^{4}}{3^{8^{2}}}$$

Add 100 and 8 to get 108.

$$\frac{\left(\frac{\left(\frac{108-3^{3}}{3}\right)^{7}}{3^{5}}\right)^{4}}{3^{8^{2}}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{\left(\frac{\left(\frac{108-27}{3}\right)^{7}}{3^{5}}\right)^{4}}{3^{8^{2}}}$$

Subtract 27 from 108 to get 81.

$$\frac{\left(\frac{\left(\frac{81}{3}\right)^{7}}{3^{5}}\right)^{4}}{3^{8^{2}}}$$

Divide 81 by 3 to get 27.

$$\frac{\left(\frac{27^{7}}{3^{5}}\right)^{4}}{3^{8^{2}}}$$

Calculate 27 to the power of 7 and get 10460353203.

$$\frac{\left(\frac{10460353203}{3^{5}}\right)^{4}}{3^{8^{2}}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{\left(\frac{10460353203}{243}\right)^{4}}{3^{8^{2}}}$$

Divide 10460353203 by 243 to get 43046721.

$$\frac{43046721^{4}}{3^{8^{2}}}$$

Calculate 43046721 to the power of 4 and get 3433683820292512484657849089281.

$$\frac{3433683820292512484657849089281}{3^{8^{2}}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{3433683820292512484657849089281}{3^{64}}$$

Calculate 3 to the power of 64 and get 3433683820292512484657849089281.

$$\frac{3433683820292512484657849089281}{3433683820292512484657849089281}$$

Divide 3433683820292512484657849089281 by 3433683820292512484657849089281 to get 1.

$$1$$

Factor

$$1$$