Solve {[(6^{3}-6^{9})^{5}:(42^{3}:7^3)^2]:6^40}^2*2

$$\{ [ ( 6 ^ { 3 } - 6 ^ { 9 } ) ^ { 5 } : ( 42 ^ { 3 } : 7 ^ { 3 } ) ^ { 2 } ] : 6 ^ { 40 } \} ^ { 2 } \cdot 2$$

Evaluate

$$\frac{48863203665627165567617586107594857751962890625}{879726203652406634807809540927942869581895303168}\approx 0.055543649$$

Solution Steps

Calculate 6 to the power of 3 and get 216.

$$\left(\frac{\frac{\left(216-6^{9}\right)^{5}}{\left(\frac{42^{3}}{7^{3}}\right)^{2}}}{6^{40}}\right)^{2}\times 2$$

Calculate 6 to the power of 9 and get 10077696.

$$\left(\frac{\frac{\left(216-10077696\right)^{5}}{\left(\frac{42^{3}}{7^{3}}\right)^{2}}}{6^{40}}\right)^{2}\times 2$$

Subtract 10077696 from 216 to get -10077480.

$$\left(\frac{\frac{\left(-10077480\right)^{5}}{\left(\frac{42^{3}}{7^{3}}\right)^{2}}}{6^{40}}\right)^{2}\times 2$$

Calculate -10077480 to the power of 5 and get -103934498432775938135902561996800000.

$$\left(\frac{\frac{-103934498432775938135902561996800000}{\left(\frac{42^{3}}{7^{3}}\right)^{2}}}{6^{40}}\right)^{2}\times 2$$

Calculate 42 to the power of 3 and get 74088.

$$\left(\frac{\frac{-103934498432775938135902561996800000}{\left(\frac{74088}{7^{3}}\right)^{2}}}{6^{40}}\right)^{2}\times 2$$

Calculate 7 to the power of 3 and get 343.

$$\left(\frac{\frac{-103934498432775938135902561996800000}{\left(\frac{74088}{343}\right)^{2}}}{6^{40}}\right)^{2}\times 2$$

Divide 74088 by 343 to get 216.

$$\left(\frac{\frac{-103934498432775938135902561996800000}{216^{2}}}{6^{40}}\right)^{2}\times 2$$

Calculate 216 to the power of 2 and get 46656.

$$\left(\frac{\frac{-103934498432775938135902561996800000}{46656}}{6^{40}}\right)^{2}\times 2$$

Divide -103934498432775938135902561996800000 by 46656 to get -2227677006875341609565812800000.

$$\left(\frac{-2227677006875341609565812800000}{6^{40}}\right)^{2}\times 2$$

Calculate 6 to the power of 40 and get 13367494538843734067838845976576.

$$\left(\frac{-2227677006875341609565812800000}{13367494538843734067838845976576}\right)^{2}\times 2$$

Reduce the fraction \frac{-2227677006875341609565812800000}{13367494538843734067838845976576} to lowest terms by extracting and canceling out 10077696.

$$\left(-\frac{221050228829619548909375}{1326443518324400147398656}\right)^{2}\times 2$$

Calculate -\frac{221050228829619548909375}{1326443518324400147398656} to the power of 2 and get \frac{48863203665627165567617586107594857751962890625}{1759452407304813269615619081855885739163790606336}.

$$\frac{48863203665627165567617586107594857751962890625}{1759452407304813269615619081855885739163790606336}\times 2$$

Multiply \frac{48863203665627165567617586107594857751962890625}{1759452407304813269615619081855885739163790606336} and 2 to get \frac{48863203665627165567617586107594857751962890625}{879726203652406634807809540927942869581895303168}.

$$\frac{48863203665627165567617586107594857751962890625}{879726203652406634807809540927942869581895303168}$$

Factor

$$\frac{5 ^ {10} \cdot 7 ^ {10} \cdot 31 ^ {10} \cdot 43 ^ {10}}{2 ^ {61} \cdot 3 ^ {62}} = 0.055543649220358746$$