Solve {[2*12^{3}:12^{2}-(2^{2}*5-54:3^{2})]*2^{3}}^{3}:[2^{3}*5+(5^4)^0-128:2^7]^3=

$$\{ [ 2 \cdot 12 ^ { 3 } : 12 ^ { 2 } - ( 2 ^ { 2 } \cdot 5 - 54 : 3 ^ { 2 } ) ] \cdot 2 ^ { 3 } \} ^ { 3 } : [ 2 ^ { 3 } \cdot 5 + ( 5 ^ { 4 } ) ^ { 0 } - 128 : 2 ^ { 7 } ] ^ { 3 } =$$

Evaluate

$$8$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 0 to get 0.

$$\frac{\left(\left(\frac{2\times 12^{3}}{12^{2}}-\left(2^{2}\times 5-\frac{54}{3^{2}}\right)\right)\times 2^{3}\right)^{3}}{\left(2^{3}\times 5+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Cancel out 12^{2} in both numerator and denominator.

$$\frac{\left(\left(2\times 12-\left(2^{2}\times 5-\frac{54}{3^{2}}\right)\right)\times 2^{3}\right)^{3}}{\left(2^{3}\times 5+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Multiply 2 and 12 to get 24.

$$\frac{\left(\left(24-\left(2^{2}\times 5-\frac{54}{3^{2}}\right)\right)\times 2^{3}\right)^{3}}{\left(2^{3}\times 5+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(\left(24-\left(4\times 5-\frac{54}{3^{2}}\right)\right)\times 2^{3}\right)^{3}}{\left(2^{3}\times 5+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Multiply 4 and 5 to get 20.

$$\frac{\left(\left(24-\left(20-\frac{54}{3^{2}}\right)\right)\times 2^{3}\right)^{3}}{\left(2^{3}\times 5+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(\left(24-\left(20-\frac{54}{9}\right)\right)\times 2^{3}\right)^{3}}{\left(2^{3}\times 5+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Divide 54 by 9 to get 6.

$$\frac{\left(\left(24-\left(20-6\right)\right)\times 2^{3}\right)^{3}}{\left(2^{3}\times 5+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Subtract 6 from 20 to get 14.

$$\frac{\left(\left(24-14\right)\times 2^{3}\right)^{3}}{\left(2^{3}\times 5+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Subtract 14 from 24 to get 10.

$$\frac{\left(10\times 2^{3}\right)^{3}}{\left(2^{3}\times 5+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(10\times 8\right)^{3}}{\left(2^{3}\times 5+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Multiply 10 and 8 to get 80.

$$\frac{80^{3}}{\left(2^{3}\times 5+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Calculate 80 to the power of 3 and get 512000.

$$\frac{512000}{\left(2^{3}\times 5+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{512000}{\left(8\times 5+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Multiply 8 and 5 to get 40.

$$\frac{512000}{\left(40+5^{0}-\frac{128}{2^{7}}\right)^{3}}$$

Calculate 5 to the power of 0 and get 1.

$$\frac{512000}{\left(40+1-\frac{128}{2^{7}}\right)^{3}}$$

Add 40 and 1 to get 41.

$$\frac{512000}{\left(41-\frac{128}{2^{7}}\right)^{3}}$$

Calculate 2 to the power of 7 and get 128.

$$\frac{512000}{\left(41-\frac{128}{128}\right)^{3}}$$

Divide 128 by 128 to get 1.

$$\frac{512000}{\left(41-1\right)^{3}}$$

Subtract 1 from 41 to get 40.

$$\frac{512000}{40^{3}}$$

Calculate 40 to the power of 3 and get 64000.

$$\frac{512000}{64000}$$

Divide 512000 by 64000 to get 8.

$$8$$

Factor

$$2^{3}$$