Question

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[tex] \frac{6 {x}^{3} {y}^{10} }{10 {x}^{ - 4}. {y}^{ - 2} } [/tex]
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Answer 1

[tex]\sf \bf \sf \frac{6 {x}^{3} {y}^{10} }{10 {x}^{ - 4}. {y}^{ - 2} } [/tex]

[tex]\sf \bf \sf (6x³ \: . \: y^{10}) ÷ (10 x^{-4} \: . \: y^{-2}[/tex]

[tex]\sf \bf \sf (6x³ ÷ 10x^{-4}) (y^{10}÷ y^{-2})[/tex]

[tex]\sf \bf \sf ((6÷10)(x³÷x^{-4})) (y^{10} ÷ y^{-2})[/tex]

[tex]\sf \bf \sf ((6÷10)(x^{3-(-4)})) (y^{10 - (-2)})[/tex]

[tex]\sf \bf \sf ((6÷10)(x^{3+4})) (y^{10 +2})[/tex]

[tex]\sf \bf \sf ((6÷10)(x^{7})) (y^{12})[/tex]

[tex]\sf \bf \sf ((6÷2)÷(10÷2)(x^{7})) (y^{12})[/tex]

[tex]\sf \bf \sf ((3÷5)(x^{7})) (y^{12})[/tex]

[tex]\sf \bf \sf \frac{3}{5}x^{7}y^{12}[/tex]

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Answer 2

Verified answer

[tex]\frac{6 {x}^{3} {y}^{10} }{10 {x}^{ - 4}{y}^{ - 2} } \\ \\ = \frac{6}{10} \times \frac{ {x}^{3} }{ {x}^{ - 4} } \times \frac{ {y}^{10} }{ {y}^{ - 2} } \\ \\ = \frac{3}{5} \times {x}^{3 + 4} \times {y}^{10 + 2} \\ \\ = \frac{3}{5} \times {x}^{7} \times {y}^{12} \\ \\ = \frac{3}{5} {x}^{7} {y}^{12} [/tex]

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