Solve (-3)^{80}:(-3)^{78}-(-7)^{25}:(4+7)^23+(-8)^3:(+5^11)^2=

$$( - 3 ) ^ { 80 } : ( - 3 ) ^ { 78 } - ( - 7 ) ^ { 25 } : ( 4 + 7 ) ^ { 23 } + ( - 8 ) ^ { 3 } : ( + 5 ^ { 11 } ) ^ { 2 } =$$

Evaluate

$$\frac{19217045922080535943362842730391679307378}{2134872062814801626793220043182373046875}\approx 9.001497681$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 78 from 80 to get 2.

$$\left(-3\right)^{2}-\frac{\left(-7\right)^{25}}{\left(4+7\right)^{23}}+\frac{\left(-8\right)^{3}}{\left(5^{11}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 11 and 2 to get 22.

$$\left(-3\right)^{2}-\frac{\left(-7\right)^{25}}{\left(4+7\right)^{23}}+\frac{\left(-8\right)^{3}}{5^{22}}$$

Calculate -3 to the power of 2 and get 9.

$$9-\frac{\left(-7\right)^{25}}{\left(4+7\right)^{23}}+\frac{\left(-8\right)^{3}}{5^{22}}$$

Calculate -7 to the power of 25 and get -1341068619663964900807.

$$9-\frac{-1341068619663964900807}{\left(4+7\right)^{23}}+\frac{\left(-8\right)^{3}}{5^{22}}$$

Add 4 and 7 to get 11.

$$9-\frac{-1341068619663964900807}{11^{23}}+\frac{\left(-8\right)^{3}}{5^{22}}$$

Calculate 11 to the power of 23 and get 895430243255237372246531.

$$9-\frac{-1341068619663964900807}{895430243255237372246531}+\frac{\left(-8\right)^{3}}{5^{22}}$$

Fraction \frac{-1341068619663964900807}{895430243255237372246531} can be rewritten as -\frac{1341068619663964900807}{895430243255237372246531} by extracting the negative sign.

$$9-\left(-\frac{1341068619663964900807}{895430243255237372246531}\right)+\frac{\left(-8\right)^{3}}{5^{22}}$$

The opposite of -\frac{1341068619663964900807}{895430243255237372246531} is \frac{1341068619663964900807}{895430243255237372246531}.

$$9+\frac{1341068619663964900807}{895430243255237372246531}+\frac{\left(-8\right)^{3}}{5^{22}}$$

Add 9 and \frac{1341068619663964900807}{895430243255237372246531} to get \frac{8060213257916800315119586}{895430243255237372246531}.

$$\frac{8060213257916800315119586}{895430243255237372246531}+\frac{\left(-8\right)^{3}}{5^{22}}$$

Calculate -8 to the power of 3 and get -512.

$$\frac{8060213257916800315119586}{895430243255237372246531}+\frac{-512}{5^{22}}$$

Calculate 5 to the power of 22 and get 2384185791015625.

$$\frac{8060213257916800315119586}{895430243255237372246531}+\frac{-512}{2384185791015625}$$

Fraction \frac{-512}{2384185791015625} can be rewritten as -\frac{512}{2384185791015625} by extracting the negative sign.

$$\frac{8060213257916800315119586}{895430243255237372246531}-\frac{512}{2384185791015625}$$

Subtract \frac{512}{2384185791015625} from \frac{8060213257916800315119586}{895430243255237372246531} to get \frac{19217045922080535943362842730391679307378}{2134872062814801626793220043182373046875}.

$$\frac{19217045922080535943362842730391679307378}{2134872062814801626793220043182373046875}$$