Josephina thinks that she has discovered a new pattern, shown at right.
Check her equations by multiplying. Does her pattern work?
To check a division problem using multiplication, multiply the divisor by the quotient. In the second case, multiply
. Does it equal How will you check the third and fourth cases?
Based on her pattern, what does
equal? Is it true? Justify your answer.
Look for a pattern in the quotients. Look at the number of terms and the exponent each term.
Make a conjecture about how to represent the result for
. You will need “…” in the middle of your expression.