Yes, product is in the scrabble dictionary

...and is worth 15 points by itself.

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Product Definition

noun

A direct result; a consequence: "Is history the product of impersonal social and economic forces?” ( Anthony Lewis).
from The American Heritage Dictionary of the English Language, 4th Edition
Chemistry A substance resulting from a chemical reaction.
from The American Heritage Dictionary of the English Language, 4th Edition
Mathematics A scalar product.
from The American Heritage Dictionary of the English Language, 4th Edition
Mathematics A vector product.
from The American Heritage Dictionary of the English Language, 4th Edition
Mathematics The number or quantity obtained by multiplying two or more numbers together.
from The American Heritage Dictionary of the English Language, 4th Edition

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Top Words by points

Points

product

12

2 letter words with PRODUCT

Points

od

3

do

3

po

4

to

2

up

4

ut

2

or

2

op

4

3 letter words with PRODUCT

Points

opt

5

orc

5

ort

3

oud

4

our

3

out

3

pod

6

pot

5

pro

5

pud

6

put

5

pur

5

cop

7

roc

5

rod

4

rot

3

rut

3

tod

4

top

5

tor

3

tup

5

udo

4

upo

5

urd

4

urp

5

duo

4

cur

5

cut

5

doc

6

dor

4

dot

4

dup

6

cup

7

cud

6

cru

5

cot

5

cor

5

cod

6

4 letter words with PRODUCT

Points

roup

6

rout

4

crop

8

coup

8

cord

7

curt

6

torc

6

tour

4

trod

5

trop

6

trou

4

updo

7

curd

7

duro

5

duct

7

drop

7

dout

5

dour

5

dorp

7

port

6

pour

6

pout

6

prod

7

crud

7

5 letter words with PRODUCT

Points

croup

9

crudo

8

proud

8

court

7

duroc

8

dropt

8

7 letter words with PRODUCT

Points

product

12

Found 77 words in 0.249 seconds