Evaluate: x5+n×(x2)3n+1x7n−2\dfrac{x^{5+n}\times(x^2)^{3n+1}}{x^{7n-2}}x7n−2x5+n×(x2)3n+1
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x5+n×(x2)3n+1x7n−2=x5+n×(x)2(3n+1)x7n−2=x5+n×(x)6n+2x7n−2=x(5+n)+(6n+2)x7n−2=x5+n+6n+2x7n−2=x(7+7n)−(7n−2)=x7+7n−7n+2=x9\dfrac{x^{5+n}\times(x^2)^{3n+1}}{x^{7n-2}}\\[1em] = \dfrac{x^{5+n}\times(x)^{2(3n+1)}}{x^{7n-2}}\\[1em] = \dfrac{x^{5+n}\times(x)^{6n+2}}{x^{7n-2}}\\[1em] = \dfrac{x^{(5+n)+(6n+2)}}{x^{7n-2}}\\[1em] = \dfrac{x^{5+n+6n+2}}{x^{7n-2}}\\[1em] = x^{(7+7n)-(7n-2)}\\[1em] = x^{7+7n-7n+2}\\[1em] = x^{9}x7n−2x5+n×(x2)3n+1=x7n−2x5+n×(x)2(3n+1)=x7n−2x5+n×(x)6n+2=x7n−2x(5+n)+(6n+2)=x7n−2x5+n+6n+2=x(7+7n)−(7n−2)=x7+7n−7n+2=x9
x5+n×(x2)3n+1x7n−2=x9\dfrac{x^{5+n}\times(x^2)^{3n+1}}{x^{7n-2}} = x^{9}x7n−2x5+n×(x2)3n+1=x9
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