a. Let p be a prime number. Fill in the second row of the table to give the number of abelian groups of order pⁿ, up to isomorphism.

b. Let p, q, and r be distinct prime numbers. Use the table you created to find the number of abelian groups, up to isomorphism, of the given order.

i. p³q⁴r⁷ 

ii. (qr)⁷

iii. q⁵r⁴q³

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n | 2 | 3 | 4 | 5 | 6 | 7 | 8 | number of groups