Question

Calculati

20⁸/21³×14⁵/45⁶×189⁴/140³×5⁶/2⁶×3³/2⁴·7³·10⁵;

Answer 1

20⁸/21³×14⁵/45⁶×189⁴/140³×5⁶/2⁶×3³/2⁴·7³·10⁵=
(2²x5)⁸/(3x7)³x(2x7)⁵/(3³x5)⁶x(7x3³)⁴/(7x2²x5)³x5⁶/2⁶x3³/(2⁴x7³x2⁵x5⁵)=
(2¹⁶x5⁸)/(3³x7³)x(2⁵x7⁵)/(3¹⁸x5⁶)x(7⁴x3¹²)/(7³x2⁶x5³)x5⁶/2⁶x3³/(2⁹x7³x5⁵)=
[(2¹⁶x5⁸x2⁵x7⁵x7⁴x3¹²x5⁶x3³)]/[(3³x7³x3¹⁸x5⁶x7³x2⁶x5³x2⁶x2⁹x7³x5⁵)]=
(2¹⁶⁺⁵x5⁸⁺⁶x7⁵⁺⁴x3¹²⁺³)/(3³⁺¹⁸x7³⁺³⁺³x5⁶⁺³⁺⁵x2⁶⁺⁶⁺⁹)=
(2¹⁹x5¹⁴x7⁹x3¹⁵)/(3²¹x7⁹x5¹⁴x2²¹)=
2¹⁹⁻²¹x5¹⁴⁻¹⁴x7⁹⁻⁹x3¹⁵⁻²¹=
2⁻²x5°x7°x3-⁶=1/4x1x1x1/729=1/2916