Take I-70 EAST to I-64 EAST to LOUISVILLE via I-270 NORTH (EXIT 232A off I-70 in MISSOURI) and I-255 SOUTH (EXIT 7 off I-270 EAST in ILLINOIS) to get onto I-255, follow signs to I-255 SOUTH to MEMPHIS; EXIT 20 off I-255 to get onto I-64, follow signs to I-64 EAST to LOUISVILLE) to bypass St. Louis. One thing, make sure you take the I-670 EAST shortcut thru downtown Kansas City (EXIT 421B off I-70 in KANSAS to get onto I-670 EAST).
Take I-64 EAST to I-57 SOUTH to MEMPHIS.
Continue SOUTH on I-57 to I-24 EAST to Nashville at EXIT 44.
Take I-24 EAST to I-40 EAST to KNOXVILLE via TN-155 - BRILEY PKWY to bypass downtown Nashville (EXIT 43 off I-24 in Tennessee to get onto BRILEY PKWY, follow signs to TN-155 - BRILEY PKWY EAST; EXIT 6A off TN-155 - BRILEY PKWY to get onto I-40 EAST to KNOXVILLE).
Take I-40 EAST to Knoxville.
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Q: How many miles are there from Topeka to Knoxville?