Xmxnm-n-xnxln-l-xlxml-m-

(x^mx^n)^m+n×(x^nx^l)^n+l×(x^lx^m)^l+m [x^mx^n=x^m n] [(x)^m n]^m+n×[(x)^n l]^n+l×[(x)^l m]^l+m [x^m× x^n=x^m+n] amp; [(a+b)(a b)=a ...

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Dividing Terms with the Same Exponent

xmxnm+n×xnxln...

Question

${(\frac{x^{m}}{x^{n}})}^{m + n} \times {(\frac{x^{n}}{x^{l}})}^{n + l} \times {(\frac{x^{l}}{x^{m}})}^{l + m}$ .

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Solution

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\frac{x^{m + n} \times x^{n + 1} \times x^{l + m}}{{(x^{m} \times x^{n} \times x^{l})}^{2}} = 1

\frac{3^{x + 1}}{3^{x (x + 1)}} \times {(\frac{3^{x}}{3})}^{x + 1} = 1

{(\frac{x^{m}}{x^{m}})}^{m + n} \cdot {(\frac{x^{n}}{x^{l}})}^{n + l} \cdot {(\frac{x^{l}}{x^{m}})}^{l + m} = 1

a = x^{m + n} y^{l}, b = x^{n + l} y^{m} and c = x^{l + m} y^{n}

a^{m - n} b^{n - l} c^{l - m} = 1

x = a^{m + n}, y = a^{n + l} and z = a^{l + m}

x^{m} y^{n} z^{l} = x^{n} y^{l} z^{m}

a = x^{m + n} . y^{l}; b = x^{n + l} . y^{m}

c = x^{l + m} . y^{n}

a^{m - n} . b^{n - l} . c^{l - m} = 1

A

B

A = \frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{c - b} + x^{a - b}} + \frac{1}{1 + x^{a - c} + x^{b - c}}

B = {(\frac{x^{m}}{x^{n}})}^{1 / (m - n)} \times {(\frac{x^{n}}{x^{l}})}^{1 / (n - l)} \times {(\frac{x^{l}}{x^{m}})}^{1 / (l - m)}

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