What is e^{1/2 ln(9)}*e^{-ln(1/3)} ?

The solution to e^{1/2 ln(9)}*e^{-ln(1/3)} is 9

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simplify e^{1/2 ln(9)}*e^{-ln(1/3)}

simplify

e^{\frac{1}{2} l n (9)} \cdot e^{- l n (\frac{1}{3})}

9

Solution steps

e^{\frac{1}{2} l n (9)} e^{- l n (\frac{1}{3})}

Apply exponent rule:

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

e^{\frac{1}{2} l n (9)} e^{- l n (\frac{1}{3})} = e^{\frac{1}{2} l n (9) - l n (\frac{1}{3})}

= e^{\frac{1}{2} l n (9) - l n (\frac{1}{3})}

Apply exponent rule:

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

= e^{\frac{1}{2} l n (9)} e^{- l n (\frac{1}{3})}

Simplify

e^{\frac{1}{2} l n (9)} : 9

= 9 e^{- l n (\frac{1}{3})}

Simplify

e^{- l n (\frac{1}{3})} : (\frac{1}{3})^{- 1}

= 9 (\frac{1}{3})^{- 1}

Simplify

= 9

2.8 \cdot 1 0^{- 4} (2.8 \cdot 1 0^{- 4})^{2}

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

1.00330545 \cdot e^{- \frac{0.00007948}{1.987 \cdot 298}}

- 4 (1.58 \cdot 1 0^{- 30}) (4105)

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

What is e^{1/2 ln(9)}*e^{-ln(1/3)} ?
The solution to e^{1/2 ln(9)}*e^{-ln(1/3)} is 9