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

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

Evaluate

$$4$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 0 and 2 to get 0.

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

Calculate 0 to the power of 5 and get 0.

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

Calculate 0 to the power of 4 and get 0.

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

Add 0 and 0 to get 0.

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

Calculate 1 to the power of 3 and get 1.

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

Calculate 1 to the power of 2 and get 1.

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

Add 1 and 1 to get 2.

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

Calculate 2 to the power of 5 and get 32.

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

Calculate 7 to the power of 0 and get 1.

$$\frac{\frac{32}{\left(1+9^{0}\right)^{3}}}{8^{0}}$$

Calculate 9 to the power of 0 and get 1.

$$\frac{\frac{32}{\left(1+1\right)^{3}}}{8^{0}}$$

Add 1 and 1 to get 2.

$$\frac{\frac{32}{2^{3}}}{8^{0}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\frac{32}{8}}{8^{0}}$$

Divide 32 by 8 to get 4.

$$\frac{4}{8^{0}}$$

Calculate 8 to the power of 0 and get 1.

$$\frac{4}{1}$$

Anything divided by one gives itself.

$$4$$

Factor

$$2^{2}$$