What is 3.7e^4*5.2e^{-5} ?

The solution to 3.7e^4*5.2e^{-5} is (19.24)/e

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simplify 3.7e^4*5.2e^{-5}

simplify

3.7 e^{4} \cdot 5.2 e^{- 5}

\frac{19.24}{e}

Decimal Notation

7.07800 \dots

Solution steps

3.7 e^{4} \cdot 5.2 e^{- 5}

Apply exponent rule:

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

e^{4} e^{- 5} = e^{4 - 5}

= 3.7 \cdot 5.2 e^{4 - 5}

Subtract the numbers:

4 - 5 = - 1

= 3.7 \cdot 5.2 e^{- 1}

Apply exponent rule:

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

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

= 3.7 \cdot 5.2 \cdot \frac{1}{e}

Multiply the numbers:

3.7 \cdot 5.2 = 19.24

= 19.24 \cdot \frac{1}{e}

Multiply fractions:

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

= \frac{1 \cdot 19.24}{e}

Multiply the numbers:

1 \cdot 19.24 = 19.24

= \frac{19.24}{e}

20 \cdot (\frac{0.1}{3})^{- \frac{1.67 - 1}{1.67}}

1 0^{- 5.8} \cdot 17 \cdot 1000

4.28 \cdot 1 0^{- 7} \frac{1}{0.63}

(2 x^{3} y^{4} z^{5}) 11 x^{2} y^{2} z^{2}