Question

$x {}^{ - 2} y {}^{5} \times x {}^{0} y {}^{ - 7}$
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Answer 1

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$\tt \: {x}^{ - 2} {y}^{5} \times {x}^{0} {y}^{ - 7} \\ \\ \tt \: (using \: identity \: {a}^{0} = 1 \: we \: will \: get) \\ \\ \tt \: = {x}^{ - 2} {y}^{5} \times 1 \times {y}^{ - 7} \\ \\ \tt \: = {x}^{ - 2} {y}^{5} {y}^{ - 7} \\ \\ \tt \: (using \: identity \: {a}^{m} {a}^{n} = {a}^{(m + n)}) \\ \\ \tt \: = {x}^{ - 2} {y}^{( - 7 + 5)} = {x}^{ - 2} {y}^{ - 2} \\ \\ \tt \: (using \: identity \: {a}^{m} {b}^{m} = {(ab)}^{m}) \\ \\ \tt \: = {(xy)}^{ - 2} \\ \\ \tt \: (using \: identity \: {a}^{ - m} = \frac{1}{ {a}^{m} }) \\ \\ \tt \: = \frac{1}{ {(xy)}^{2} }$

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