Answer:
1/18
Step-by-step explanation:
[tex]( {2}^{ - 3} \times {16}^{ \frac{1}{2} } ) \div ( {81}^{ \frac{3}{4} } \times {27}^{ - \frac{1}{3} } ) \\ \\ =( {2}^{ - 3} \times {2}^{ \frac{4 \times 1}{2} } ) \div ( {3}^{ \frac{4 \times 3}{4} } \times {3}^{ - \frac{3 \times 1}{3} } ) \\ \\=( {2}^{ - 3} \times {2}^{ 2} ) \div ( {3}^{ 3 } \times {3}^{ - 1 } ) \\ \\=( {2}^{ - 3 + 2} ) \div ( {3}^{ 3 - 1 } ) \\ \\ = {2}^{ - 1} \div {3}^{2} \\ \\ = \frac{1}{2} \times \frac{1}{9} \\ \\ = \frac{1}{18} [/tex]
