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Popular >

simplify ce^{rt}*ce^{-rt}

Solution

simplify

c e^{r t} \cdot c e^{- r t}

Solution

c^{2}

Solution steps

c e^{r t} c e^{- r t}

Apply exponent rule:

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

cc = c^{1 + 1}

= e^{r t} c^{1 + 1} e^{- r t}

Add the numbers:

1 + 1 = 2

= e^{r t} c^{2} e^{- r t}

Apply exponent rule:

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

e^{r t} e^{- r t} = e^{r t - r t}

= c^{2} e^{r t - r t}

Add similar elements:

r t - r t = 0

= c^{2} e^{0}

Apply rule

a^{0} = 1, a \neq = 0

e^{0} = 1

= 1 \cdot c^{2}

Multiply:

c^{2} \cdot 1 = c^{2}

= c^{2}

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Frequently Asked Questions (FAQ)

What is ce^{rt}*ce^{-rt} ?
The solution to ce^{rt}*ce^{-rt} is c^2