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Answer 1

$10) \: \sqrt{6} \times \sqrt{7} \\ = \sqrt{42} \\ 11) {x}^{ {a}^{2} - {b}^{2} } \times {x}^{ {b}^{2} - {c}^{2} } \times {x}^{ {c}^{2} - {a}^{2} } \\ = {x}^{ {a}^{2} - {b}^{2} + {b}^{2} - {c}^{2} + {c}^{2} - {a}^{2} } \\ = {x}^{0} = 1 \\ 12) \: {81}^{ \frac{ - 1}{4} } \\ = ( { {3}^{4} )}^{ \frac{ - 1}{4} } = {3}^{4 \times \frac{ - 1}{4} } = {3}^{ - 1} = \frac{1}{3} \\ {32}^{ \frac{2}{5} } = { ({2}^{5}) }^{ \frac{2}{5} } \\ = {2}^{2} = 4 \: \: \: ans \\ 13)a) \: {x}^{3} - 5x + 2 \: \: is \: polynomial \\ b) \: 2 \sqrt{x} + 7 \: \: \: is \: not \: a \: polynomial$
polynomial does not have negative powers and rational numbers