SAT Mathematics Practice Test 6

Number 16 can be written in exponential form ${\mathit{a}}^{\frac{\mathit{b}}{4}}$ where a and b are positive integers as follows: $2^4,4^2,{16}^1,{\left({16}^2\right)}^{\frac{1}{2}},{\left({16}^4\right)}^{\frac{1}{4}}$ Hence,if ${\mathit{a}}^{\frac{\mathit{b}}{4}}=16$ where a and b are positive integers, then $\frac{\mathit{b}}{4}$ can be $4,2,1,\frac{1}{2}$ or $\frac{1}{4}$ So the value of b can be16, 8, 4, 2, or 1. Any of these values may be gridded as the correct answer.