What is 1400*4pi*10^{-7}*15*15 ?

The solution to 1400*4pi*10^{-7}*15*15 is (63pi)/(500)

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simplify 14004pi10^{-7}1515

Solution

simplify

1400 \cdot 4 π \cdot 1 0^{- 7} \cdot 15 \cdot 15

Solution

\frac{63 π}{500}

Decimal Notation

0.39584 \dots

Solution steps

1400 \cdot 4 π 1 0^{- 7} \cdot 15 \cdot 15

Apply exponent rule:

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

15 \cdot 15 = 1 5^{1 + 1}

= 1400 \cdot 4 π 1 0^{- 7} \cdot 1 5^{1 + 1}

Add the numbers:

1 + 1 = 2

= 1400 \cdot 4 π 1 0^{- 7} \cdot 1 5^{2}

Factor integer

1400 = 5^{2} \cdot 56

= 5^{2} \cdot 56 \cdot 4 π 1 0^{- 7} \cdot 1 5^{2}

Factor integer

10 = 5 \cdot 2

= 5^{2} \cdot 56 \cdot 4 π (5 \cdot 2)^{- 7} \cdot 1 5^{2}

Apply exponent rule:

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

(5 \cdot 2)^{- 7} = 5^{- 7} \cdot 2^{- 7}

= 5^{2} \cdot 56 \cdot 4 π 5^{- 7} \cdot 2^{- 7} \cdot 1 5^{2}

Factor integer

15 = 5 \cdot 3

= 5^{2} \cdot 56 \cdot 4 π 5^{- 7} \cdot 2^{- 7} (5 \cdot 3)^{2}

Apply exponent rule:

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

(5 \cdot 3)^{2} = 5^{2} \cdot 3^{2}

= 5^{2} \cdot 56 \cdot 4 π 5^{- 7} \cdot 2^{- 7} \cdot 5^{2} \cdot 3^{2}

Apply exponent rule:

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

5^{2} \cdot 5^{- 7} \cdot 5^{2} = 5^{2 - 7 + 2}

= 56 \cdot 4 π 2^{- 7} \cdot 5^{2 - 7 + 2} \cdot 3^{2}

Add/Subtract the numbers:

2 - 7 + 2 = - 3

= 56 \cdot 4 π 2^{- 7} \cdot 5^{- 3} \cdot 3^{2}

Apply exponent rule:

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

2^{- 7} = \frac{1}{2 ^{7}}

= 5^{- 3} \cdot 3^{2} \cdot 56 \cdot 4 π \frac{1}{2 ^{7}}

Apply exponent rule:

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

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

= 3^{2} \cdot 56 \cdot 4 π \frac{1}{2 ^{7}} \cdot \frac{1}{5 ^{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 \cdot 56 \cdot 4 π 3 ^{2}}{2 ^{7} \cdot 5 ^{3}}

Multiply the numbers:

1 \cdot 1 \cdot 56 \cdot 4 = 224

= \frac{3 ^{2} \cdot 224 π}{2 ^{7} \cdot 5 ^{3}}

Factor

224 : 2^{5} \cdot 7

= \frac{2 ^{5} \cdot 3 ^{2} \cdot 7 π}{2 ^{7} \cdot 5 ^{3}}

Cancel

\frac{2 ^{5} \cdot 7 π 3 ^{2}}{2 ^{7} \cdot 5 ^{3}} : \frac{3 ^{2} \cdot 7 π}{5 ^{3} \cdot 2 ^{2}}

= \frac{3 ^{2} \cdot 7 π}{5 ^{3} \cdot 2 ^{2}}

3^{2} \cdot 7 π = 63 π

= \frac{63 π}{5 ^{3} \cdot 2 ^{2}}

5^{3} \cdot 2^{2} = 500

= \frac{63 π}{500}

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Frequently Asked Questions (FAQ)

What is 1400*4pi*10^{-7}*15*15 ?
The solution to 1400*4pi*10^{-7}*15*15 is (63pi)/(500)

simplify 1400*4pi*10^{-7}*15*15

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 1400*4pi*10^{-7}*15*15 ?

simplify 14004pi10^{-7}1515

What is 14004pi10^{-7}1515 ?