Solve frac{7^{10}+7^38-2*7^99}{6^2*49^19}

$$\frac { 7 ^ { 10 } + 7 ^ { 38 } - 2 \cdot 7 ^ { 99 } } { 6 ^ { 2 } \cdot 49 ^ { 19 } }$$

Evaluate

$$-\frac{90876806304135272693175608837659889500428609708610930541759432266114100067}{459986536544739960976801}\approx -1.97564057 \cdot 10^{50}$$

Solution Steps

Calculate 7 to the power of 10 and get 282475249.

$$\frac{282475249+7^{38}-2\times 7^{99}}{6^{2}\times 49^{19}}$$

Calculate 7 to the power of 38 and get 129934811447123020117172145698449.

$$\frac{282475249+129934811447123020117172145698449-2\times 7^{99}}{6^{2}\times 49^{19}}$$

Add 282475249 and 129934811447123020117172145698449 to get 129934811447123020117172428173698.

$$\frac{129934811447123020117172428173698-2\times 7^{99}}{6^{2}\times 49^{19}}$$

Calculate 7 to the power of 99 and get 462068072803536855906378252728602401551029028414946485847699333055955922805275437143.

$$\frac{129934811447123020117172428173698-2\times 462068072803536855906378252728602401551029028414946485847699333055955922805275437143}{6^{2}\times 49^{19}}$$

Multiply 2 and 462068072803536855906378252728602401551029028414946485847699333055955922805275437143 to get 924136145607073711812756505457204803102058056829892971695398666111911845610550874286.

$$\frac{129934811447123020117172428173698-924136145607073711812756505457204803102058056829892971695398666111911845610550874286}{6^{2}\times 49^{19}}$$

Subtract 924136145607073711812756505457204803102058056829892971695398666111911845610550874286 from 129934811447123020117172428173698 to get -924136145607073711812756505457204803102058056829892841760587218988891728438122700588.

$$\frac{-924136145607073711812756505457204803102058056829892841760587218988891728438122700588}{6^{2}\times 49^{19}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{-924136145607073711812756505457204803102058056829892841760587218988891728438122700588}{36\times 49^{19}}$$

Calculate 49 to the power of 19 and get 129934811447123020117172145698449.

$$\frac{-924136145607073711812756505457204803102058056829892841760587218988891728438122700588}{36\times 129934811447123020117172145698449}$$

Multiply 36 and 129934811447123020117172145698449 to get 4677653212096428724218197245144164.

$$\frac{-924136145607073711812756505457204803102058056829892841760587218988891728438122700588}{4677653212096428724218197245144164}$$

Reduce the fraction \frac{-924136145607073711812756505457204803102058056829892841760587218988891728438122700588}{4677653212096428724218197245144164} to lowest terms by extracting and canceling out 10169108964.

$$-\frac{90876806304135272693175608837659889500428609708610930541759432266114100067}{459986536544739960976801}$$