Solve [(0^{5}+0^{4}+1^{3}+1^{2})^{5}:(7^{0}+9^9)^3]:(8^9)^2=

$$[ ( 0 ^ { 5 } + 0 ^ { 4 } + 1 ^ { 3 } + 1 ^ { 2 } ) ^ { 5 } : ( 7 ^ { 0 } + 9 ^ { 9 } ) ^ { 3 } ] : ( 8 ^ { 9 } ) ^ { 2 } =$$

Evaluate

$$\frac{1}{32735391990810248958045594675197247488000}\approx 3.054797695 \cdot 10^{-41}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\frac{\frac{\left(0^{5}+0^{4}+1^{3}+1^{2}\right)^{5}}{\left(7^{0}+9^{9}\right)^{3}}}{8^{18}}$$

Calculate 0 to the power of 5 and get 0.

$$\frac{\frac{\left(0+0^{4}+1^{3}+1^{2}\right)^{5}}{\left(7^{0}+9^{9}\right)^{3}}}{8^{18}}$$

Calculate 0 to the power of 4 and get 0.

$$\frac{\frac{\left(0+0+1^{3}+1^{2}\right)^{5}}{\left(7^{0}+9^{9}\right)^{3}}}{8^{18}}$$

Add 0 and 0 to get 0.

$$\frac{\frac{\left(1^{3}+1^{2}\right)^{5}}{\left(7^{0}+9^{9}\right)^{3}}}{8^{18}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{\frac{\left(1+1^{2}\right)^{5}}{\left(7^{0}+9^{9}\right)^{3}}}{8^{18}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{\frac{\left(1+1\right)^{5}}{\left(7^{0}+9^{9}\right)^{3}}}{8^{18}}$$

Add 1 and 1 to get 2.

$$\frac{\frac{2^{5}}{\left(7^{0}+9^{9}\right)^{3}}}{8^{18}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{\frac{32}{\left(7^{0}+9^{9}\right)^{3}}}{8^{18}}$$

Calculate 7 to the power of 0 and get 1.

$$\frac{\frac{32}{\left(1+9^{9}\right)^{3}}}{8^{18}}$$

Calculate 9 to the power of 9 and get 387420489.

$$\frac{\frac{32}{\left(1+387420489\right)^{3}}}{8^{18}}$$

Add 1 and 387420489 to get 387420490.

$$\frac{\frac{32}{387420490^{3}}}{8^{18}}$$

Calculate 387420490 to the power of 3 and get 58149737453323966743649000.

$$\frac{\frac{32}{58149737453323966743649000}}{8^{18}}$$

Reduce the fraction \frac{32}{58149737453323966743649000} to lowest terms by extracting and canceling out 8.

$$\frac{\frac{4}{7268717181665495842956125}}{8^{18}}$$

Calculate 8 to the power of 18 and get 18014398509481984.

$$\frac{\frac{4}{7268717181665495842956125}}{18014398509481984}$$

Express \frac{\frac{4}{7268717181665495842956125}}{18014398509481984} as a single fraction.

$$\frac{4}{7268717181665495842956125\times 18014398509481984}$$

Multiply 7268717181665495842956125 and 18014398509481984 to get 130941567963240995832182378700788989952000.

$$\frac{4}{130941567963240995832182378700788989952000}$$

Reduce the fraction \frac{4}{130941567963240995832182378700788989952000} to lowest terms by extracting and canceling out 4.

$$\frac{1}{32735391990810248958045594675197247488000}$$

Factor

$$\frac{1}{2 ^ {52} \cdot 5 ^ {3} \cdot 73 ^ {3} \cdot 530713 ^ {3}} = 3.054797695047392 \times 10^{-41}$$