Solve 146*20*19*18*7^145/3*2*8^146*1000

$$\frac{ 146 \times 20 \times 19 \times 18 \times { 7 }^{ 145 } }{ 3 \times 2 \times { 8 }^{ 146 } } \times 1000$$

Evaluate

$$\frac{900105748261256169727075488565509420822854167998533942563489437096725329864117609424368558284785021251705751334264800808876204375}{11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296}\approx 0.081158761$$

Solution Steps

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{6\times 19\times 20\times 73\times 7^{145}}{8^{146}}\times 1000$$

Multiply 6 and 19 to get 114.

$$\frac{114\times 20\times 73\times 7^{145}}{8^{146}}\times 1000$$

Multiply 114 and 20 to get 2280.

$$\frac{2280\times 73\times 7^{145}}{8^{146}}\times 1000$$

Multiply 2280 and 73 to get 166440.

$$\frac{166440\times 7^{145}}{8^{146}}\times 1000$$

Calculate 7 to the power of 145 and get 346111318725789442817428690628410255543515181157811657798986565574323606773032486200189784488261483778593896211204922204807.

$$\frac{166440\times 346111318725789442817428690628410255543515181157811657798986565574323606773032486200189784488261483778593896211204922204807}{8^{146}}\times 1000$$

Multiply 166440 and 346111318725789442817428690628410255543515181157811657798986565574323606773032486200189784488261483778593896211204922204807 to get 57606767888720394862532831268192602932662666751906172324063323974190421111303527003159587730226241360109168085392947251768077080.

$$\frac{57606767888720394862532831268192602932662666751906172324063323974190421111303527003159587730226241360109168085392947251768077080}{8^{146}}\times 1000$$

Calculate 8 to the power of 146 and get 709803441694928604052074031140629428079727891296209043243642772637343054798240159498233447962659731992932150006119314388217384402944.

$$\frac{57606767888720394862532831268192602932662666751906172324063323974190421111303527003159587730226241360109168085392947251768077080}{709803441694928604052074031140629428079727891296209043243642772637343054798240159498233447962659731992932150006119314388217384402944}\times 1000$$

Reduce the fraction \frac{57606767888720394862532831268192602932662666751906172324063323974190421111303527003159587730226241360109168085392947251768077080}{709803441694928604052074031140629428079727891296209043243642772637343054798240159498233447962659731992932150006119314388217384402944} to lowest terms by extracting and canceling out 8.

$$\frac{7200845986090049357816603908524075366582833343988271540507915496773802638912940875394948466278280170013646010674118406471009635}{88725430211866075506509253892578678509965986412026130405455346579667881849780019937279180995332466499116518750764914298527173050368}\times 1000$$

Express \frac{7200845986090049357816603908524075366582833343988271540507915496773802638912940875394948466278280170013646010674118406471009635}{88725430211866075506509253892578678509965986412026130405455346579667881849780019937279180995332466499116518750764914298527173050368}\times 1000 as a single fraction.

$$\frac{7200845986090049357816603908524075366582833343988271540507915496773802638912940875394948466278280170013646010674118406471009635\times 1000}{88725430211866075506509253892578678509965986412026130405455346579667881849780019937279180995332466499116518750764914298527173050368}$$

Multiply 7200845986090049357816603908524075366582833343988271540507915496773802638912940875394948466278280170013646010674118406471009635 and 1000 to get 7200845986090049357816603908524075366582833343988271540507915496773802638912940875394948466278280170013646010674118406471009635000.

$$\frac{7200845986090049357816603908524075366582833343988271540507915496773802638912940875394948466278280170013646010674118406471009635000}{88725430211866075506509253892578678509965986412026130405455346579667881849780019937279180995332466499116518750764914298527173050368}$$

Reduce the fraction \frac{7200845986090049357816603908524075366582833343988271540507915496773802638912940875394948466278280170013646010674118406471009635000}{88725430211866075506509253892578678509965986412026130405455346579667881849780019937279180995332466499116518750764914298527173050368} to lowest terms by extracting and canceling out 8.

$$\frac{900105748261256169727075488565509420822854167998533942563489437096725329864117609424368558284785021251705751334264800808876204375}{11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296}$$

Factor

$$\frac{3 \cdot 5 ^ {4} \cdot 7 ^ {145} \cdot 19 \cdot 73}{2 ^ {432}} = 0.08115876101017781$$