Question

A and B are two positive integers, such that A power B × B power A = 800, Find 'a' and 'b'.​

Answer 1

Answer:

${a}^{b} \times {b}^{a} = 800$

${a}^{b} \times {b}^{a} = 2 \times 2 \times 2 \times 2 \times 5 \times 5$

${a}^{b} \times {b}^{a} = {2}^{5} \times {5}^{2}$

so a=2

and b=5