What is 10^4*10^{-8}*2pi*sqrt(6) ?

The solution to 10^4*10^{-8}*2pi*sqrt(6) is (sqrt(3)pi)/(2500sqrt(2))

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Popular >

simplify 10^410^{-8}2pi*sqrt(6)

Solution

simplify

1 0^{4} \cdot 1 0^{- 8} \cdot 2 π \cdot 6

Solution

\frac{3 π}{2500 2}

Decimal Notation

0.00153 \dots

Solution steps

1 0^{4} \cdot 1 0^{- 8} \cdot 2 π 6

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

1 0^{4} \cdot 1 0^{- 8} = 1 0^{4 - 8}

= 1 0^{4 - 8} \cdot 2 π 6

Subtract the numbers:

4 - 8 = - 4

= 1 0^{- 4} \cdot 2 π 6

Factor integer

10 = 2 \cdot 5

= (2 \cdot 5)^{- 4} \cdot 2 π 6

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(2 \cdot 5)^{- 4} = 2^{- 4} \cdot 5^{- 4}

= 2^{- 4} \cdot 5^{- 4} \cdot 2 π 6

Factor integer

6 = 2 \cdot 3

= 2^{- 4} \cdot 5^{- 4} \cdot 2 π 2 \cdot 3

Apply radical rule:

2 \cdot 3 = 23

= 2^{- 4} \cdot 5^{- 4} \cdot 2 π 23

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2^{- 4} \cdot 2 = 2^{- 4 + 1}

= 5^{- 4} \cdot 2^{- 4 + 1} π 23

Add/Subtract the numbers:

- 4 + 1 = - 3

= 5^{- 4} \cdot 2^{- 3} π 23

Apply exponent rule:

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

5^{- 4} = \frac{1}{5 ^{4}}

= 2^{- 3} 23 π \frac{1}{5 ^{4}}

Apply exponent rule:

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

2^{- 3} = \frac{1}{2 ^{3}}

= 23 π \frac{1}{5 ^{4}} \cdot \frac{1}{2 ^{3}}

Multiply fractions:

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

= \frac{1 \cdot 1 π 2 3}{5 ^{4} \cdot 2 ^{3}}

Multiply:

1 \cdot 1 π 23 = π 23

= \frac{2 3 π}{5 ^{4} \cdot 2 ^{3}}

Apply radical rule:

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

= \frac{2 ^{\frac{1}{2}} 3 π}{5 ^{4} \cdot 2 ^{3}}

Apply exponent rule:

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

\frac{2 ^{\frac{1}{2}}}{2 ^{3}} = \frac{1}{2 ^{3 - \frac{1}{2}}}

= \frac{3 π}{5 ^{4} \cdot 2 ^{- \frac{1}{2} + 3}}

Subtract the numbers:

3 - \frac{1}{2} = \frac{5}{2}

= \frac{3 π}{5 ^{4} \cdot 2 ^{\frac{5}{2}}}

2^{\frac{5}{2}} = 2^{2} 2

= \frac{3 π}{5 ^{4} \cdot 2 ^{2} 2}

5^{4} \cdot 2^{2} 2 = 25002

= \frac{3 π}{2500 2}

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Frequently Asked Questions (FAQ)

What is 10^4*10^{-8}*2pi*sqrt(6) ?
The solution to 10^4*10^{-8}*2pi*sqrt(6) is (sqrt(3)pi)/(2500sqrt(2))

simplify 10^4*10^{-8}*2pi*sqrt(6)

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 10^4*10^{-8}*2pi*sqrt(6) ?

simplify 10^410^{-8}2pi*sqrt(6)

What is 10^410^{-8}2pi*sqrt(6) ?