What is 82(40(2pi))^2(4.1*10^{-3}) ?

The solution to 82(40(2pi))^2(4.1*10^{-3}) is 21236.23039…

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simplify 82(40(2pi))^2(4.1*10^{-3})

simplify

82 (40 (2 π))^{2} (4.1 \cdot 1 0^{- 3})

21236.23039 \dots

Solution steps

82 (40 (2 π))^{2} (4.1 \cdot 1 0^{- 3})

Apply exponent rule:

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

= 82 \cdot 4.1 \cdot \frac{1}{1 0 ^{3}} (40 \cdot 2 π)^{2}

(40 \cdot 2 π)^{2} = 8 0^{2} π^{2}

= 8 0^{2} \cdot 82 \cdot 4.1 π^{2} \frac{1}{1 0 ^{3}}

Multiply fractions:

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

= 4.1 \cdot \frac{8 0 ^{2} \cdot 1 \cdot 82 π ^{2}}{1 0 ^{3}}

\frac{1 \cdot 82 \cdot 8 0 ^{2} π ^{2}}{1 0 ^{3}} = \frac{2624 π ^{2}}{5}

= 4.1 \cdot \frac{2624 π ^{2}}{5}

Multiply fractions:

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

= \frac{2624 π ^{2} \cdot 4.1}{5}

Multiply the numbers:

2624 \cdot 4.1 = 10758.4

= \frac{10758.4 π ^{2}}{5}

Convert element to a decimal form

π^{2} = 9.86960 \dots

= \frac{9.86960 \dots \cdot 10758.4}{5}

Multiply the numbers:

10758.4 \cdot 9.86960 \dots = 106181.15198 \dots

= \frac{106181.15198 \dots}{5}

Divide the numbers:

\frac{106181.15198 \dots}{5} = 21236.23039 \dots

= 21236.23039 \dots

e^{- 0.03} (0.55075 \cdot 10.24 + 0.44925 \cdot 50.27)

(\frac{1}{44000} + \frac{1}{6000})^{- 1} \cdot 10 \cdot 1 0^{- 6} \cdot 555.556

b^{4} (3 a b^{3}) (2 a^{2} b^{5})

2 (x + 3) (x - 1)

0.43 \cdot 5.67 \cdot 1 0^{- 8} \cdot (1390.4)^{4}

What is 82(40(2pi))^2(4.1*10^{-3}) ?
The solution to 82(40(2pi))^2(4.1*10^{-3}) is 21236.23039…