Answer: The ascending order is given below.
Step-by-step explanation: We are given five exponents and we are to arrange them in ascending order.
We have
\(32^\frac{3}{5}=\left(2^5\right)^\frac{3}{5}=2^{5\times\frac{3}{5}}=2^3=8.\)
\(64^\frac{2}{3}=\left(2^6\right)^\frac{2}{3}=2^{6\times\frac{2}{3}}=2^4=16.\)
\(81^\frac{1}{4}=\left(3^4\right)^\frac{1}{4}=3^{4\times\frac{1}{4}}=3.\)
\(49^\frac{1}{2}=\left(7^2\right)^\frac{1}{2}=7^{2\times\frac{1}{2}}=7.\)
\(125^\frac{2}{3}=\left(5^3\right)^\frac{2}{3}=5^{3\times\frac{2}{3}}=5^2=25.\)
Since 3 < 7 < 8 <16 < 25, so we have
\(81^\frac{1}{4}<49^\frac{1}{2}<32^\frac{3}{5}<64^\frac{2}{3}<125^\frac{2}{3}.\)
