What is 1995*((400)/(sqrt(418.8)))^{-1.6} ?

The solution to 1995*((400)/(sqrt(418.8)))^{-1.6} is 17.14953…

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simplify 1995*((400)/(sqrt(418.8)))^{-1.6}

simplify

1995 \cdot (\frac{400}{418.8})^{- 1.6}

17.14953 \dots

Solution steps

1995 (\frac{400}{418.8})^{- 1.6}

Apply exponent rule:

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

= 1995 \cdot \frac{1}{( \frac{400}{418.8} ) ^{1.6}}

\frac{1}{( \frac{400}{418.8} ) ^{1.6}} = \frac{418. 8 ^{0.8}}{40 0 ^{1.6}}

= 1995 \cdot \frac{418. 8 ^{0.8}}{40 0 ^{1.6}}

Multiply fractions:

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

= \frac{418. 8 ^{0.8} \cdot 1995}{40 0 ^{1.6}}

Factor

1995 : 3 \cdot 5 \cdot 7 \cdot 19

Factor

40 0^{1.6} : 2^{6.4} \cdot 5^{3.2}

= \frac{3 \cdot 5 \cdot 7 \cdot 19 \cdot 418. 8 ^{0.8}}{2 ^{6.4} \cdot 5 ^{3.2}}

Cancel

\frac{418. 8 ^{0.8} \cdot 3 \cdot 5 \cdot 7 \cdot 19}{2 ^{6.4} \cdot 5 ^{3.2}} : \frac{3 \cdot 7 \cdot 19 \cdot 418. 8 ^{0.8}}{2 ^{6.4} \cdot 5 ^{2.2}}

= \frac{3 \cdot 7 \cdot 19 \cdot 418. 8 ^{0.8}}{2 ^{6.4} \cdot 5 ^{2.2}}

Multiply the numbers:

3 \cdot 7 \cdot 19 = 399

= \frac{399 \cdot 418. 8 ^{0.8}}{2 ^{6.4} \cdot 5 ^{2.2}}

2^{6.4} = 84.44850 \dots

= \frac{399 \cdot 418. 8 ^{0.8}}{5 ^{2.2} \cdot 84.44850 \dots}

418. 8^{0.8} = 125.20029 \dots

= \frac{399 \cdot 125.20029 \dots}{5 ^{2.2} \cdot 84.44850 \dots}

5^{2.2} = 34.49324 \dots

= \frac{399 \cdot 125.20029 \dots}{34.49324 \dots \cdot 84.44850 \dots}

Multiply the numbers:

399 \cdot 125.20029 \dots = 49954.91612 \dots

= \frac{49954.91612 \dots}{34.49324 \dots \cdot 84.44850 \dots}

Multiply the numbers:

84.44850 \dots \cdot 34.49324 \dots = 2912.90272 \dots

= \frac{49954.91612 \dots}{2912.90272 \dots}

Divide the numbers:

\frac{49954.91612 \dots}{2912.90272 \dots} = 17.14953 \dots

= 17.14953 \dots

e^{- j \cdot \frac{2 π}{8} \cdot 7}

, (u^{3}) u^{2}

4.7 8^{2} + 2^{2} \cdot (10 - 4. 8^{2})^{2} + 3^{2}

20 \cdot e^{(- \frac{1}{10} \cdot 1)}

What is 1995*((400)/(sqrt(418.8)))^{-1.6} ?
The solution to 1995*((400)/(sqrt(418.8)))^{-1.6} is 17.14953…