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Popular >

simplify-4pi10^{-7}4

Solution

simplify

- 4 π \cdot 1 0^{- 7} \cdot 4

Solution

- \frac{π}{625000}

+1

Solution steps

- 4 π 1 0^{- 7} \cdot 4

Apply exponent rule:

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

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

= - π 1 0^{- 7} \cdot 4^{1 + 1}

Add the numbers:

1 + 1 = 2

= - π 1 0^{- 7} \cdot 4^{2}

Factor integer

10 = 2 \cdot 5

= - π (2 \cdot 5)^{- 7} \cdot 4^{2}

Apply exponent rule:

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

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

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

Factor integer

4 = 2^{2}

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

Apply exponent rule:

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

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

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

Refine

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

Apply exponent rule:

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

2^{- 7} \cdot 2^{4} = 2^{- 7 + 4}

= - π 5^{- 7} \cdot 2^{- 7 + 4}

Add/Subtract the numbers:

- 7 + 4 = - 3

= - π 5^{- 7} \cdot 2^{- 3}

Apply exponent rule:

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

5^{- 7} = \frac{1}{5 ^{7}}

= 2^{- 3} π \frac{1}{5 ^{7}}

Apply exponent rule:

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

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

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

Multiply:

1 \cdot 1 π = π

= - \frac{π}{5 ^{7} \cdot 2 ^{3}}

5^{7} \cdot 2^{3} = 625000

= - \frac{π}{625000}

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Frequently Asked Questions (FAQ)

What is simplify-4pi*10^{-7}*4 ?
The solution to simplify-4pi*10^{-7}*4 is -pi/(625000)