Question

(x^2×y^3)^3×(x^3×y^4)^5
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(x^2×y^2)^4​

Answer 1

Step-by-step explanation:

$\frac{ ({ {x}^{2} \times {y}^{3} ) }^{3} \times( { {x}^{3} \times {y}^{4} )}^{5} }{ { ({x}^{2} \times {y}^{2} )}^{4} } \\ \\ = \frac{ {x}^{6} \times {y}^{9} \times {x}^{15} \times {y}^{20} }{ {x}^{8} \times {y}^{8} } \\ \\ = \frac{ {x}^{6 + 15} \times {y}^{9 + 20} }{ {x}^{8} \times {y}^{8} } \\ \\ = \frac{ {x}^{21} \times {y}^{29} }{ {x}^{8} \times {y}^{8} } \\ \\ = {x}^{21 - 8} \times {y}^{29 - 8} \\ \\ = {x}^{13} \times {y}^{21} \\ \\ \\ using \: formula \: (xy) {}^{m} = {x}^{m} \times {y}^{m} \\ \\ ( {x}^{m} ) {}^{n} = {x}^{ m\times n} \\ \\ {x}^{m} \times {x}^{n} = {x}^{ m+n } \\ \\ \frac{ {x}^{m} }{ {x}^{n} } = {x}^{ m- n}$