Solve [(27^{17}+3^{51}-5^{34}+25^17):(-5^49)+(-625^32):(-125)^42]*(-7)

$$[ ( 27 ^ { 17 } + 3 ^ { 51 } - 5 ^ { 34 } + 25 ^ { 17 } ) : ( - 5 ^ { 49 } ) + ( - 625 ^ { 32 } ) : ( - 125 ) ^ { 42 } ] \cdot ( - 7 )$$

Evaluate

$$\frac{3108624468980590028669226479382647333}{17763568394002504646778106689453125}=175.000000002$$

Solution Steps

Calculate 27 to the power of 17 and get 2153693963075557766310747.

$$\left(\frac{2153693963075557766310747+3^{51}-5^{34}+25^{17}}{-5^{49}}+\frac{-625^{32}}{\left(-125\right)^{42}}\right)\left(-7\right)$$

Calculate 3 to the power of 51 and get 2153693963075557766310747.

$$\left(\frac{2153693963075557766310747+2153693963075557766310747-5^{34}+25^{17}}{-5^{49}}+\frac{-625^{32}}{\left(-125\right)^{42}}\right)\left(-7\right)$$

Add 2153693963075557766310747 and 2153693963075557766310747 to get 4307387926151115532621494.

$$\left(\frac{4307387926151115532621494-5^{34}+25^{17}}{-5^{49}}+\frac{-625^{32}}{\left(-125\right)^{42}}\right)\left(-7\right)$$

Calculate 5 to the power of 34 and get 582076609134674072265625.

$$\left(\frac{4307387926151115532621494-582076609134674072265625+25^{17}}{-5^{49}}+\frac{-625^{32}}{\left(-125\right)^{42}}\right)\left(-7\right)$$

Subtract 582076609134674072265625 from 4307387926151115532621494 to get 3725311317016441460355869.

$$\left(\frac{3725311317016441460355869+25^{17}}{-5^{49}}+\frac{-625^{32}}{\left(-125\right)^{42}}\right)\left(-7\right)$$

Calculate 25 to the power of 17 and get 582076609134674072265625.

$$\left(\frac{3725311317016441460355869+582076609134674072265625}{-5^{49}}+\frac{-625^{32}}{\left(-125\right)^{42}}\right)\left(-7\right)$$

Add 3725311317016441460355869 and 582076609134674072265625 to get 4307387926151115532621494.

$$\left(\frac{4307387926151115532621494}{-5^{49}}+\frac{-625^{32}}{\left(-125\right)^{42}}\right)\left(-7\right)$$

Calculate 5 to the power of 49 and get 17763568394002504646778106689453125.

$$\left(\frac{4307387926151115532621494}{-17763568394002504646778106689453125}+\frac{-625^{32}}{\left(-125\right)^{42}}\right)\left(-7\right)$$

Fraction \frac{4307387926151115532621494}{-17763568394002504646778106689453125} can be rewritten as -\frac{4307387926151115532621494}{17763568394002504646778106689453125} by extracting the negative sign.

$$\left(-\frac{4307387926151115532621494}{17763568394002504646778106689453125}+\frac{-625^{32}}{\left(-125\right)^{42}}\right)\left(-7\right)$$

Calculate 625 to the power of 32 and get 293873587705571876992184134305561419454666389193021880377187926569604314863681793212890625.

$$\left(-\frac{4307387926151115532621494}{17763568394002504646778106689453125}+\frac{-293873587705571876992184134305561419454666389193021880377187926569604314863681793212890625}{\left(-125\right)^{42}}\right)\left(-7\right)$$

Calculate -125 to the power of 42 and get 11754943508222875079687365372222456778186655567720875215087517062784172594547271728515625.

$$\left(-\frac{4307387926151115532621494}{17763568394002504646778106689453125}+\frac{-293873587705571876992184134305561419454666389193021880377187926569604314863681793212890625}{11754943508222875079687365372222456778186655567720875215087517062784172594547271728515625}\right)\left(-7\right)$$

Divide -293873587705571876992184134305561419454666389193021880377187926569604314863681793212890625 by 11754943508222875079687365372222456778186655567720875215087517062784172594547271728515625 to get -25.

$$\left(-\frac{4307387926151115532621494}{17763568394002504646778106689453125}-25\right)\left(-7\right)$$

Convert 25 to fraction \frac{444089209850062616169452667236328125}{17763568394002504646778106689453125}.

$$\left(-\frac{4307387926151115532621494}{17763568394002504646778106689453125}-\frac{444089209850062616169452667236328125}{17763568394002504646778106689453125}\right)\left(-7\right)$$

Since -\frac{4307387926151115532621494}{17763568394002504646778106689453125} and \frac{444089209850062616169452667236328125}{17763568394002504646778106689453125} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4307387926151115532621494-444089209850062616169452667236328125}{17763568394002504646778106689453125}\left(-7\right)$$

Subtract 444089209850062616169452667236328125 from -4307387926151115532621494 to get -444089209854370004095603782768949619.

$$-\frac{444089209854370004095603782768949619}{17763568394002504646778106689453125}\left(-7\right)$$

Express -\frac{444089209854370004095603782768949619}{17763568394002504646778106689453125}\left(-7\right) as a single fraction.

$$\frac{-444089209854370004095603782768949619\left(-7\right)}{17763568394002504646778106689453125}$$

Multiply -444089209854370004095603782768949619 and -7 to get 3108624468980590028669226479382647333.

$$\frac{3108624468980590028669226479382647333}{17763568394002504646778106689453125}$$

Factor

$$\frac{7 \cdot 11 ^ {2} \cdot 31 \cdot 43 \cdot 2089 \cdot 1318002583147112110927347047}{5 ^ {49}} = 175\frac{3.0151864965421904 \times 10^{25}}{1.7763568394002505 \times 10^{34}} = 175.0000000016974$$