Solve (-15)^{3}:5^{3}-[9*4:(-6)-14]:5*5^{2}+{[(-20^{2})^{4}:(5)^8]:(-4)^6-2^3}*(-2)^3

$$( - 15 ) ^ { 3 } : 5 ^ { 3 } - [ 9 \cdot 4 : ( - 6 ) - 14 ] : 5 \cdot 5 ^ { 2 } + \{ [ ( - 20 ^ { 2 } ) ^ { 4 } : ( 5 ) ^ { 8 } ] : ( - 4 ) ^ { 6 } - 2 ^ { 3 } \} \cdot ( - 2 ) ^ { 3 }$$

Evaluate

$$9$$

Solution Steps

Calculate -15 to the power of 3 and get -3375.

$$\frac{-3375}{5^{3}}-\frac{\frac{9\times 4}{-6}-14}{5}\times 5^{2}+\left(\frac{\frac{\left(-20^{2}\right)^{4}}{5^{8}}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{-3375}{125}-\frac{\frac{9\times 4}{-6}-14}{5}\times 5^{2}+\left(\frac{\frac{\left(-20^{2}\right)^{4}}{5^{8}}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Divide -3375 by 125 to get -27.

$$-27-\frac{\frac{9\times 4}{-6}-14}{5}\times 5^{2}+\left(\frac{\frac{\left(-20^{2}\right)^{4}}{5^{8}}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Multiply 9 and 4 to get 36.

$$-27-\frac{\frac{36}{-6}-14}{5}\times 5^{2}+\left(\frac{\frac{\left(-20^{2}\right)^{4}}{5^{8}}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Divide 36 by -6 to get -6.

$$-27-\frac{-6-14}{5}\times 5^{2}+\left(\frac{\frac{\left(-20^{2}\right)^{4}}{5^{8}}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Subtract 14 from -6 to get -20.

$$-27-\frac{-20}{5}\times 5^{2}+\left(\frac{\frac{\left(-20^{2}\right)^{4}}{5^{8}}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Divide -20 by 5 to get -4.

$$-27-\left(-4\times 5^{2}\right)+\left(\frac{\frac{\left(-20^{2}\right)^{4}}{5^{8}}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Calculate 5 to the power of 2 and get 25.

$$-27-\left(-4\times 25\right)+\left(\frac{\frac{\left(-20^{2}\right)^{4}}{5^{8}}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Multiply -4 and 25 to get -100.

$$-27-\left(-100\right)+\left(\frac{\frac{\left(-20^{2}\right)^{4}}{5^{8}}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

The opposite of -100 is 100.

$$-27+100+\left(\frac{\frac{\left(-20^{2}\right)^{4}}{5^{8}}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Add -27 and 100 to get 73.

$$73+\left(\frac{\frac{\left(-20^{2}\right)^{4}}{5^{8}}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Calculate 20 to the power of 2 and get 400.

$$73+\left(\frac{\frac{\left(-400\right)^{4}}{5^{8}}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Calculate -400 to the power of 4 and get 25600000000.

$$73+\left(\frac{\frac{25600000000}{5^{8}}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Calculate 5 to the power of 8 and get 390625.

$$73+\left(\frac{\frac{25600000000}{390625}}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Divide 25600000000 by 390625 to get 65536.

$$73+\left(\frac{65536}{\left(-4\right)^{6}}-2^{3}\right)\left(-2\right)^{3}$$

Calculate -4 to the power of 6 and get 4096.

$$73+\left(\frac{65536}{4096}-2^{3}\right)\left(-2\right)^{3}$$

Divide 65536 by 4096 to get 16.

$$73+\left(16-2^{3}\right)\left(-2\right)^{3}$$

Calculate 2 to the power of 3 and get 8.

$$73+\left(16-8\right)\left(-2\right)^{3}$$

Subtract 8 from 16 to get 8.

$$73+8\left(-2\right)^{3}$$

Calculate -2 to the power of 3 and get -8.

$$73+8\left(-8\right)$$

Multiply 8 and -8 to get -64.

$$73-64$$

Subtract 64 from 73 to get 9.

$$9$$

Factor

$$3^{2}$$