What is (1e^{3x})/9 e^{-3x} ?

The solution to (1e^{3x})/9 e^{-3x} is 1/9

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simplify (1e^{3x})/9 e^{-3x}

simplify

\frac{1 e ^{3 x}}{9} e^{- 3 x}

\frac{1}{9}

Decimal Notation

0.11111 \dots

Solution steps

\frac{1 \cdot e ^{3 x}}{9} e^{- 3 x}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1 \cdot e ^{3 x}}{9} \cdot \frac{1}{e ^{3 x}}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot e ^{3 x} \cdot 1}{9 e ^{3 x}}

Cancel the common factor:

e^{3 x}

= \frac{1 \cdot 1}{9}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{9}

(3) e^{- l n (2)}

(x^{\circ})^{\frac{8}{3}} x

e^{- 2 c}

2 x^{2} (2 y)