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By using the basic rules of exponents, plus the fact that the exponential function (e raised to some power) and the natural logarithm are inverse functions.

e8 ln x + cos x

= e8 ln x ecosx

= e(ln x)(8) ecosx

= (eln x)8 ecosx

= (eln x)8 ecosx

= x8 ecosx

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Q: How do you simplify e raised to 8 ln x plus cos x?
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