Question

simplify : (81)^1/4 - 8×(216)^1/3 + 15×(32)^1/5 + √225

Answer 1

${(81)}^{ \frac{1}{4} } - 8 \times {(216)}^{ \frac{1}{3} } + 15 \times {(32)}^{ \frac{1}{5} } + \sqrt{ {(15)}^{2} } \\ \\ = {( {3}^{4}) }^{ \frac{1}{4} } - 8 \times { ({6}^{3} )}^{ \frac{1}{3} } + 15 \times { ({2}^{5} )}^{ \frac{1}{5} } + 15 \\ \\ = {(3)}^{4 \times \frac{1}{4} } - 8 \times {(6)}^{3 \times \frac{1}{3} } + 15 \times {(2)}^{5 \times \frac{1}{5} } + 15 \: \: \: \: \: \: \: [ { {(a}^{m}) }^{n} = {(a)}^{mn} ] \\ \\ = 3 - 8 \times 6 + 15 \times 2 + 15 \\ \\ = 3 - 48 + 30 + 15 \\ \\ = 48 - 48 = 0$