Alan

I get the following:

16^(5/4) → (16^(1/4))^5 → 2^5 → 32

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Depends on the expression and the exponent!  Do you have a specific example in mind?

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(1/2)log₂ 36 → log₂ 36^1/2 → log₂ 6

So:  (1/2)log₂ 36 - log₂ 3 →  log₂ 6 -  log₂ 3 → log₂(6/3) → log₂ 2 → 1

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As follows:

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log(1/10) = log(10^-1) = -1*log(10) = -1  (Assuming log is log to the base 10)

In step 4) I should have said: "... the two-thousand-five-hundredth root ..."  not "...the one-thousand-two-hundred-and-fiftyth root...".  I obviously had a senior moment!!!

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It might help to think of the meaning in stages as follows:

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This is just an expression involving x, y and z.  What do you want to do with it?

If you want to factor it the result is: 3y(x + 2z - 3y)

I'll assume this is f(x,y) = y(x)*x + 1 + b  where b is a constant, y is a function of x and you want df/dx:

df/dx = y(x)*dx/dx + x*dy(x)/dx +d(1+b)/dx  → y(x) + x*dy(x)/dx

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