Hi! I am working on homework and came across this problem:(adsbygoogle = window.adsbygoogle || []).push({});

<n|X^{5}|n>

I know X = ((ħ/(2mω))^{1/2}(a + a^{+}))

And if I raise X to the 5th, its becomes X^{5}= ((ħ/(2mω))^{5/2}(a + a^{+})^{5})

What I'm wondering is, is there anyway to be able to solve this without going through all of the iterations the raising and lowering operators will create being raised to the 5th power? Or will I just have to tackle every strain this will produce?

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# I Raising the ladder operators to a power

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