What is sqrt(9e^4)*2e^{-3} ?

The solution to sqrt(9e^4)*2e^{-3} is 6/e

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simplify sqrt(9e^4)*2e^{-3}

simplify

9 e^{4} \cdot 2 e^{- 3}

\frac{6}{e}

Decimal Notation

2.20727 \dots

Solution steps

9 e^{4} \cdot 2 e^{- 3}

Apply exponent rule:

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

= 2 \cdot \frac{1}{e ^{3}} 9 e^{4}

9 e^{4} = 3 e^{2}

= 3 \cdot 2 e^{2} \frac{1}{e ^{3}}

Multiply fractions:

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

= \frac{1 \cdot 3 e ^{2} \cdot 2}{e ^{3}}

Multiply the numbers:

1 \cdot 3 \cdot 2 = 6

= \frac{6 e ^{2}}{e ^{3}}

Apply exponent rule:

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

\frac{e ^{2}}{e ^{3}} = \frac{1}{e ^{3 - 2}}

= \frac{6}{e ^{3 - 2}}

Subtract the numbers:

3 - 2 = 1

= \frac{6}{e}

(\frac{50}{4.002 \cdot 1 0 ^{- 3}}) \cdot 1 0^{- 6}

400 e^{- 3 \cdot 0.23}

(5^{4})^{3^{^{'}}}

9 e^{x} \cdot 2 e^{x}

(x - 6)^{2} (x + 3)^{2}