What is 0.5*200^{0.5}*50^{-0.5} ?

The solution to 0.5*200^{0.5}*50^{-0.5} is 200^{0.5}*1/(10sqrt(2))

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simplify 0.5200^{0.5}50^{-0.5}

simplify

0.5 \cdot 20 0^{0.5} \cdot 5 0^{- 0.5}

20 0^{0.5} \cdot \frac{1}{10 2}

Decimal Notation

1

Solution steps

0.5 \cdot 20 0^{0.5} \cdot 5 0^{- 0.5}

5 0^{- 0.5} = \frac{1}{5 \cdot 2 ^{\frac{1}{2}}}

= 0.5 \cdot 20 0^{0.5} \cdot \frac{1}{5 \cdot 2 ^{\frac{1}{2}}}

0.5 \cdot 20 0^{0.5} \cdot \frac{1}{5 \cdot 2 ^{\frac{1}{2}}} = \frac{0.5}{2 ^{\frac{1}{2}} \cdot 5} \cdot 20 0^{0.5}

= \frac{0.5}{2 ^{\frac{1}{2}} \cdot 5} \cdot 20 0^{0.5}

\frac{0.5}{2 ^{\frac{1}{2}} \cdot 5} = \frac{5}{50 \cdot 2 ^{\frac{1}{2}}}

= \frac{5}{50 \cdot 2 ^{\frac{1}{2}}} \cdot 20 0^{0.5}

Cancel the numbers:

\frac{5}{50} = \frac{1}{10}

= \frac{1}{10 \cdot 2 ^{\frac{1}{2}}} \cdot 20 0^{0.5}

= 20 0^{0.5} \cdot \frac{1}{10 \cdot 2 ^{\frac{1}{2}}}

Apply exponent rule:

a^{\frac{1}{2}} = a

2^{\frac{1}{2}} = 2

= 20 0^{0.5} \cdot \frac{1}{10 2}

0.8256 (5)^{- 0.04}

184000 \cdot 4.14 \cdot 1 0^{- 5}

(1 - e cos (θ) + \frac{e ^{2}}{4})^{- 1}

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

6 (x + 5)^{2} (x + 2) (x - 1)^{2}

What is 0.5*200^{0.5}*50^{-0.5} ?
The solution to 0.5*200^{0.5}*50^{-0.5} is 200^{0.5}*1/(10sqrt(2))