What is 1140*((400)/(sqrt(418.8)))^{-1.6} ?

The solution to 1140*((400)/(sqrt(418.8)))^{-1.6} is 9.79973…

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simplify 1140*((400)/(sqrt(418.8)))^{-1.6}

simplify

1140 \cdot (\frac{400}{418.8})^{- 1.6}

9.79973 \dots

Solution steps

1140 (\frac{400}{418.8})^{- 1.6}

Apply exponent rule:

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

= 1140 \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}}

= 1140 \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 1140}{40 0 ^{1.6}}

Factor

1140 : 2^{2} \cdot 3 \cdot 5 \cdot 19

Factor

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

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

Cancel

\frac{418. 8 ^{0.8} \cdot 2 ^{2} \cdot 3 \cdot 5 \cdot 19}{2 ^{6.4} \cdot 5 ^{3.2}} : \frac{3 \cdot 19 \cdot 418. 8 ^{0.8}}{2 ^{4.4} \cdot 5 ^{2.2}}

= \frac{3 \cdot 19 \cdot 418. 8 ^{0.8}}{2 ^{4.4} \cdot 5 ^{2.2}}

Multiply the numbers:

3 \cdot 19 = 57

= \frac{57 \cdot 418. 8 ^{0.8}}{2 ^{4.4} \cdot 5 ^{2.2}}

2^{4.4} = 21.11212 \dots

= \frac{57 \cdot 418. 8 ^{0.8}}{5 ^{2.2} \cdot 21.11212 \dots}

418. 8^{0.8} = 125.20029 \dots

= \frac{57 \cdot 125.20029 \dots}{5 ^{2.2} \cdot 21.11212 \dots}

5^{2.2} = 34.49324 \dots

= \frac{57 \cdot 125.20029 \dots}{21.11212 \dots \cdot 34.49324 \dots}

Multiply the numbers:

57 \cdot 125.20029 \dots = 7136.41658 \dots

= \frac{7136.41658 \dots}{21.11212 \dots \cdot 34.49324 \dots}

Multiply the numbers:

21.11212 \dots \cdot 34.49324 \dots = 728.22568 \dots

= \frac{7136.41658 \dots}{728.22568 \dots}

Divide the numbers:

\frac{7136.41658 \dots}{728.22568 \dots} = 9.79973 \dots

= 9.79973 \dots

12 e^{- 0.04 \cdot \frac{8}{12}}

(- 1)^{2} e^{- (- 1)^{2}}

e^{\frac{1}{3} t} \cdot e^{- \frac{1}{3} t}

(6.63 \cdot 1 0^{- 34}) \cdot (600 \cdot 1 0^{12})

(1.6 x 1 0^{- 19}) (8 x 1 0^{6}) (2.5) (sin (6 0^{\circ}))

What is 1140*((400)/(sqrt(418.8)))^{-1.6} ?
The solution to 1140*((400)/(sqrt(418.8)))^{-1.6} is 9.79973…