What is (x^3e^{x^2})(e^{2x^2}) ?

The solution to (x^3e^{x^2})(e^{2x^2}) is e^{3x^2}x^3

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simplify (x^3e^{x^2})(e^{2x^2})

simplify

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

e^{3 x^{2}} x^{3}

Solution steps

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{x^{2}} e^{2 x^{2}} = e^{x^{2} + 2 x^{2}}

= x^{3} e^{x^{2} + 2 x^{2}}

Add similar elements:

x^{2} + 2 x^{2} = 3 x^{2}

= x^{3} e^{3 x^{2}}

(x + 1)^{2} (x + 4)^{2}

e^{- 9999999999}

(2)^{t} \cdot (1.5)^{t}

What is (x^3e^{x^2})(e^{2x^2}) ?
The solution to (x^3e^{x^2})(e^{2x^2}) is e^{3x^2}x^3