Solve {l}{(-6+2)^{3}-80:(-12-4)+(-2)^{76}:(-2)^{7}}{-6^{2}-24:[3^{8^{2}}:(-3^9)^7+(-9)^23:(-3*3^43)]}

$$\left. \begin{array} { l } { ( - 6 + 2 ) ^ { 3 } - 80 : ( - 12 - 4 ) + ( - 2 ) ^ { 76 } : ( - 2 ) ^ { 7 } } \\ { - 6 ^ { 2 } - 24 : [ 3 ^ { 8 ^ { 2 } } : ( - 3 ^ { 9 } ) ^ { 7 } + ( - 9 ) ^ { 23 } : ( - 3 \cdot 3 ^ { 43 } ) ] } \end{array} \right.$$

Evaluate

$$-590295810358705651811$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 76 to get 69.

$$\left(-6+2\right)^{3}-\frac{80}{-12-4}+\left(-2\right)^{69}-6^{2}-\frac{24}{\frac{3^{8^{2}}}{\left(-3^{9}\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Add -6 and 2 to get -4.

$$\left(-4\right)^{3}-\frac{80}{-12-4}+\left(-2\right)^{69}-6^{2}-\frac{24}{\frac{3^{8^{2}}}{\left(-3^{9}\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Calculate -4 to the power of 3 and get -64.

$$-64-\frac{80}{-12-4}+\left(-2\right)^{69}-6^{2}-\frac{24}{\frac{3^{8^{2}}}{\left(-3^{9}\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Subtract 4 from -12 to get -16.

$$-64-\frac{80}{-16}+\left(-2\right)^{69}-6^{2}-\frac{24}{\frac{3^{8^{2}}}{\left(-3^{9}\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Divide 80 by -16 to get -5.

$$-64-\left(-5\right)+\left(-2\right)^{69}-6^{2}-\frac{24}{\frac{3^{8^{2}}}{\left(-3^{9}\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

The opposite of -5 is 5.

$$-64+5+\left(-2\right)^{69}-6^{2}-\frac{24}{\frac{3^{8^{2}}}{\left(-3^{9}\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Add -64 and 5 to get -59.

$$-59+\left(-2\right)^{69}-6^{2}-\frac{24}{\frac{3^{8^{2}}}{\left(-3^{9}\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Calculate -2 to the power of 69 and get -590295810358705651712.

$$-59-590295810358705651712-6^{2}-\frac{24}{\frac{3^{8^{2}}}{\left(-3^{9}\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Subtract 590295810358705651712 from -59 to get -590295810358705651771.

$$-590295810358705651771-6^{2}-\frac{24}{\frac{3^{8^{2}}}{\left(-3^{9}\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Calculate 6 to the power of 2 and get 36.

$$-590295810358705651771-36-\frac{24}{\frac{3^{8^{2}}}{\left(-3^{9}\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Subtract 36 from -590295810358705651771 to get -590295810358705651807.

$$-590295810358705651807-\frac{24}{\frac{3^{8^{2}}}{\left(-3^{9}\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Calculate 8 to the power of 2 and get 64.

$$-590295810358705651807-\frac{24}{\frac{3^{64}}{\left(-3^{9}\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Calculate 3 to the power of 64 and get 3433683820292512484657849089281.

$$-590295810358705651807-\frac{24}{\frac{3433683820292512484657849089281}{\left(-3^{9}\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Calculate 3 to the power of 9 and get 19683.

$$-590295810358705651807-\frac{24}{\frac{3433683820292512484657849089281}{\left(-19683\right)^{7}}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Calculate -19683 to the power of 7 and get -1144561273430837494885949696427.

$$-590295810358705651807-\frac{24}{\frac{3433683820292512484657849089281}{-1144561273430837494885949696427}+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Divide 3433683820292512484657849089281 by -1144561273430837494885949696427 to get -3.

$$-590295810358705651807-\frac{24}{-3+\frac{\left(-9\right)^{23}}{-3\times 3^{43}}}$$

Calculate -9 to the power of 23 and get -8862938119652501095929.

$$-590295810358705651807-\frac{24}{-3+\frac{-8862938119652501095929}{-3\times 3^{43}}}$$

Calculate 3 to the power of 43 and get 328256967394537077627.

$$-590295810358705651807-\frac{24}{-3+\frac{-8862938119652501095929}{-3\times 328256967394537077627}}$$

Multiply -3 and 328256967394537077627 to get -984770902183611232881.

$$-590295810358705651807-\frac{24}{-3+\frac{-8862938119652501095929}{-984770902183611232881}}$$

Divide -8862938119652501095929 by -984770902183611232881 to get 9.

$$-590295810358705651807-\frac{24}{-3+9}$$

Add -3 and 9 to get 6.

$$-590295810358705651807-\frac{24}{6}$$

Divide 24 by 6 to get 4.

$$-590295810358705651807-4$$

Subtract 4 from -590295810358705651807 to get -590295810358705651811.

$$-590295810358705651811$$

Factor

$$-590295810358705651811$$