Question

A and b are positive integers. Find −2a+3b if a^3*b^2=72.

Answer 1

${a}^{3} {b}^{2} = a \times a \times a \times b \times b \\ 72 = 2 \times 2 \times 2 \times 3 \times 3 = {2}^{3} {3}^{2} \\ {a}^{3} {b}^{2} = 72 \\ \Rightarrow a = 2,b = 3 \\ \Rightarrow - 2a + 3b = - 2 \times 2 + 3 \times 3 = - 4 + 9 = 5$