What is (e^{n^2})/(e^{(n+1)^2)} ?

The solution to (e^{n^2})/(e^{(n+1)^2)} is e^{-2n-1}

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simplify (e^{n^2})/(e^{(n+1)^2)}

simplify

\frac{e ^{n^{2}}}{e ^{(n + 1)^{2}}}

e^{- 2 n - 1}

Solution steps

\frac{e ^{n^{2}}}{e ^{(n + 1)^{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

= e^{n^{2} - (n + 1)^{2}}

Expand

n^{2} - (n + 1)^{2} : - 2 n - 1

= e^{- 2 n - 1}

x^{5 x}

(2 x^{3}) (10 x)

(2 x^{4} y^{3}) (3 x y^{2})

400 π \cdot 33 \cdot 1 0^{- 3}

What is (e^{n^2})/(e^{(n+1)^2)} ?
The solution to (e^{n^2})/(e^{(n+1)^2)} is e^{-2n-1}