Answer:
[tex]x^{m} x^{n} x^{p}[/tex]
Step-by-step explanation:
[tex](x^{m+n})^{2} = x^{2m+2n} = x^{2m}x^{2n}\\\\(x^{n+p})^{2} = x^{2n+2p} = x^{2n}x^{2p}\\\\(x^{p+m})^{2} = x^{2p+2m} = x^{2p}x^{2m}\\\\\\\\[/tex]
Numerator = [tex]x^{2m}x^{2n} . x^{2n}x^{2p} . x^{2p}x^{2m} = x^{4m} x^{4n} x^{4p}[/tex]
Denominator = [tex]x^{3m+3n+3p} = x^{3m} x^{3n}x^{3p}[/tex]
And therefore
[tex]\frac{x^{4m} x^{4n} x^{4p}}{x^{3m} x^{3n}x^{3p}} = x^{m} x^{n} x^{p}[/tex]
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Verified answer
Answer:
[tex]x^{m} x^{n} x^{p}[/tex]
Step-by-step explanation:
[tex](x^{m+n})^{2} = x^{2m+2n} = x^{2m}x^{2n}\\\\(x^{n+p})^{2} = x^{2n+2p} = x^{2n}x^{2p}\\\\(x^{p+m})^{2} = x^{2p+2m} = x^{2p}x^{2m}\\\\\\\\[/tex]
Numerator = [tex]x^{2m}x^{2n} . x^{2n}x^{2p} . x^{2p}x^{2m} = x^{4m} x^{4n} x^{4p}[/tex]
Denominator = [tex]x^{3m+3n+3p} = x^{3m} x^{3n}x^{3p}[/tex]
And therefore
[tex]\frac{x^{4m} x^{4n} x^{4p}}{x^{3m} x^{3n}x^{3p}} = x^{m} x^{n} x^{p}[/tex]