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### $e^(-alog(x1)/(a+b)+alog(x1)/(a+b)+a*log(x2)/(a+b)-alog(x3)/(a+b))$ does not simplify in sage

I'm running the following code in sage but the answer is not simplified all the way:

eq=e^(-a*log(x1)/(a+b)+a*log(x1)/(a+b)+a*log(x2)/(a+b)-a*log(x4)/(a+b))
eq
Out: [e^(a*log(x2)/(a + b) - a*log(x3)/(a + b))]
show(eq)


$$e^{\left(\frac{alog(x2)}{a + b} - \frac{alog(x3)}{a + b}\right)}$$

what I wanted to get is along the lines of $$\left(\frac{x_2}{x_3}\right)^\frac{1}{a+b}$$

I've tried using simplify_full() with no success. any help is appreciated.

### $e^(-alog(x1)/(a+b)+alog(x1)/(a+b)+a*log(x2)/(a+b)-alog(x3)/(a+b))$ does not simplify in sage

I'm running the following code in sage but the answer is not simplified all the way:

eq=e^(-a*log(x1)/(a+b)+a*log(x1)/(a+b)+a*log(x2)/(a+b)-a*log(x4)/(a+b))
eq
Out: [e^(a*log(x2)/(a + b) - a*log(x3)/(a + b))]
show(eq)


$$e^{\left(\frac{alog(x2)}{a + b} - \frac{alog(x3)}{a + b}\right)}$$

what I wanted to get is along the lines of $$\left(\frac{x_2}{x_3}\right)^\frac{1}{a+b}$$

I've tried using simplify_full() with no success. any help is appreciated.

### $e^(-alog(x1)/(a+b)+alog(x1)/(a+b)+a*log(x2)/(a+b)-alog(x3)/(a+b))$ $e^{\frac{-alog(x1)}{a+b}+\frac{alog(x1)}{a+b}+\frac{alog(x2)}{a+b}-\frac{alog(x3)}{a+b}}$ does not simplify in sage

I'm running the following code in sage but the answer is not simplified all the way:

eq=e^(-a*log(x1)/(a+b)+a*log(x1)/(a+b)+a*log(x2)/(a+b)-a*log(x4)/(a+b))
eq
Out: [e^(a*log(x2)/(a + b) - a*log(x3)/(a + b))]
show(eq)


$$e^{\left(\frac{alog(x2)}{a + b} - \frac{alog(x3)}{a + b}\right)}$$

what I wanted to get is along the lines of $$\left(\frac{x_2}{x_3}\right)^\frac{1}{a+b}$$

I've tried using simplify_full() with no success. any help is appreciated.

### $e^{\frac{-alog(x1)}{a+b}+\frac{alog(x1)}{a+b}+\frac{alog(x2)}{a+b}-\frac{alog(x3)}{a+b}}$ $e^\left({\frac{-alog(x1)}{a+b}+\frac{alog(x1)}{a+b}+\frac{alog(x2)}{a+b}-\frac{alog(x3)}{a+b}}\right)$ does not simplify in sage

I'm running the following code in sage but the answer is not simplified all the way:

eq=e^(-a*log(x1)/(a+b)+a*log(x1)/(a+b)+a*log(x2)/(a+b)-a*log(x4)/(a+b))
eq=e^(-a*log(x1)/(a+b)+a*log(x1)/(a+b)+a*log(x2)/(a+b)-a*log(x3)/(a+b))
eq
Out: [e^(a*log(x2)/(a + b) - a*log(x3)/(a + b))]
show(eq)


$$e^{\left(\frac{alog(x2)}{a + b} - \frac{alog(x3)}{a + b}\right)}$$

what I wanted to get is along the lines of $$\left(\frac{x_2}{x_3}\right)^\frac{1}{a+b}$$

I've tried using simplify_full() with no success. any help is appreciated.