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Popular >

simplify ye^{-1/2 x}(ye^{1/2 x})

Solution

simplify

y \cdot e^{- \frac{1}{2} x} (y \cdot e^{\frac{1}{2} x})

Solution

y^{2}

Solution steps

y e^{- \frac{1}{2} x} (y e^{\frac{1}{2} x})

Apply exponent rule:

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

e^{- \frac{1}{2} x} e^{\frac{1}{2} x} = e^{- \frac{1}{2} x + \frac{1}{2} x}

= yy e^{- \frac{1}{2} x + \frac{1}{2} x}

Apply exponent rule:

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

yy = y^{1 + 1}

= y^{1 + 1} e^{- \frac{1}{2} x + \frac{1}{2} x}

Add the numbers:

1 + 1 = 2

= y^{2} e^{- \frac{1}{2} x + \frac{1}{2} x}

e^{- \frac{1}{2} x + \frac{1}{2} x} = 1

= 1 \cdot y^{2}

Multiply:

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

= y^{2}

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Frequently Asked Questions (FAQ)

What is y*e^{-1/2 x}(y*e^{1/2 x}) ?
The solution to y*e^{-1/2 x}(y*e^{1/2 x}) is y^2