Solve -[(-2)^{10}:(+4)^{3}-5^3*3^3]:(2^6:4-15^3)

$$- [ ( - 2 ) ^ { 10 } : ( + 4 ) ^ { 3 } - 5 ^ { 3 } \cdot 3 ^ { 3 } ] : ( 2 ^ { 6 } : 4 - 15 ^ { 3 } )$$

Evaluate

$$-1$$

Solution Steps

Calculate -2 to the power of 10 and get 1024.

$$\frac{-\left(\frac{1024}{4^{3}}-5^{3}\times 3^{3}\right)}{\frac{2^{6}}{4}-15^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{-\left(\frac{1024}{64}-5^{3}\times 3^{3}\right)}{\frac{2^{6}}{4}-15^{3}}$$

Divide 1024 by 64 to get 16.

$$\frac{-\left(16-5^{3}\times 3^{3}\right)}{\frac{2^{6}}{4}-15^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{-\left(16-125\times 3^{3}\right)}{\frac{2^{6}}{4}-15^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{-\left(16-125\times 27\right)}{\frac{2^{6}}{4}-15^{3}}$$

Multiply 125 and 27 to get 3375.

$$\frac{-\left(16-3375\right)}{\frac{2^{6}}{4}-15^{3}}$$

Subtract 3375 from 16 to get -3359.

$$\frac{-\left(-3359\right)}{\frac{2^{6}}{4}-15^{3}}$$

The opposite of -3359 is 3359.

$$\frac{3359}{\frac{2^{6}}{4}-15^{3}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{3359}{\frac{64}{4}-15^{3}}$$

Divide 64 by 4 to get 16.

$$\frac{3359}{16-15^{3}}$$

Calculate 15 to the power of 3 and get 3375.

$$\frac{3359}{16-3375}$$

Subtract 3375 from 16 to get -3359.

$$\frac{3359}{-3359}$$

Divide 3359 by -3359 to get -1.

$$-1$$

Factor

$$-1$$