What is 1200((600)/(sqrt(234.98)))^{-1.6} ?

The solution to 1200((600)/(sqrt(234.98)))^{-1.6} is 3.39597…

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simplify 1200((600)/(sqrt(234.98)))^{-1.6}

simplify

1200 (\frac{600}{234.98})^{- 1.6}

3.39597 \dots

Solution steps

1200 (\frac{600}{234.98})^{- 1.6}

Apply exponent rule:

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

= 1200 \cdot \frac{1}{( \frac{600}{234.98} ) ^{1.6}}

\frac{1}{( \frac{600}{234.98} ) ^{1.6}} = \frac{234.9 8 ^{0.8}}{60 0 ^{1.6}}

= 1200 \cdot \frac{234.9 8 ^{0.8}}{60 0 ^{1.6}}

Multiply fractions:

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

= \frac{234.9 8 ^{0.8} \cdot 1200}{60 0 ^{1.6}}

Factor

1200 : 2^{4} \cdot 5^{2} \cdot 3

Factor

60 0^{1.6} : 2^{4.8} \cdot 5^{3.2} \cdot 3^{1.6}

= \frac{2 ^{4} \cdot 5 ^{2} \cdot 3 \cdot 234.9 8 ^{0.8}}{2 ^{4.8} \cdot 5 ^{3.2} \cdot 3 ^{1.6}}

Cancel

\frac{234.9 8 ^{0.8} \cdot 2 ^{4} \cdot 3 \cdot 5 ^{2}}{2 ^{4.8} \cdot 3 ^{1.6} \cdot 5 ^{3.2}} : \frac{234.9 8 ^{0.8}}{5 ^{1.2} \cdot 2 ^{0.8} \cdot 3 ^{0.6}}

= \frac{234.9 8 ^{0.8}}{5 ^{1.2} \cdot 2 ^{0.8} \cdot 3 ^{0.6}}

5^{1.2} = 6.89864 \dots

= \frac{234.9 8 ^{0.8}}{2 ^{0.8} \cdot 3 ^{0.6} \cdot 6.89864 \dots}

234.9 8^{0.8} = 78.85417 \dots

= \frac{78.85417 \dots}{2 ^{0.8} \cdot 3 ^{0.6} \cdot 6.89864 \dots}

2^{0.8} = 1.74110 \dots

= \frac{78.85417 \dots}{3 ^{0.6} \cdot 1.74110 \dots \cdot 6.89864 \dots}

3^{0.6} = 1.93318 \dots

= \frac{78.85417 \dots}{1.74110 \dots \cdot 1.93318 \dots \cdot 6.89864 \dots}

Multiply the numbers:

6.89864 \dots \cdot 1.74110 \dots \cdot 1.93318 \dots = 23.21992 \dots

= \frac{78.85417 \dots}{23.21992 \dots}

Divide the numbers:

\frac{78.85417 \dots}{23.21992 \dots} = 3.39597 \dots

= 3.39597 \dots

60 e^{- 4}

6 \cdot 62

(6 m n^{3}) (36 m^{4} n^{2}) (4 m^{5} n^{5})

What is 1200((600)/(sqrt(234.98)))^{-1.6} ?
The solution to 1200((600)/(sqrt(234.98)))^{-1.6} is 3.39597…