# Fractional exponents - adding the exponent?

I have this question for which I need to simplify the expression so that only positive exponents occur, and assuming the variables are positive:

$$x^{2/5} x^{1/4} x^{-1/2}$$

The answer is supposed to be $x^{3/20}$ I think, but I keep getting $1/x^{1/20}$

Can anyone please help me with how I can get to the answer? Much appreciated!!

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Are you writing $2/5=0.2$? –  Michael Jul 8 at 0:32
I mistakenly changed the fraction 2/5 to 4/20 hence why i was always resulting in -1/20. Solved the issue - thanks everyone! –  Dani Jul 8 at 0:35

## 2 Answers

$$\huge{x^{\frac{2}{5}}x^{\frac{1}{4}}x^{\frac{-1}{2}}=x^{\frac{2}{5}+\frac{1}{4}-\frac{1}{2}}=x^{\frac{8+5-10}{20}}=x^{\frac{3}{20}}}$$

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THANK YOU!!! I made the silliest mistake by changing the 2/5 to 4/20. Thanks a million! –  Dani Jul 8 at 0:34
YOU'RE WELCOME!!! –  user71352 Jul 8 at 0:35

Hint: Use $a^{m_1} \cdot a^{m_2} \cdot \ldots \cdot a^{m_n}=a^{m_1+m_2+...+m_n}$.

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