What is 5.67*10^{-8}*4pi(7*10^8)^2*5780^4 ?

The solution to 5.67*10^{-8}*4pi(7*10^8)^2*5780^4 is 3.89673E26

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Popular >

simplify 5.6710^{-8}4pi(710^8)^25780^4

Solution

simplify

5.67 \cdot 1 0^{- 8} \cdot 4 π (7 \cdot 1 0^{8})^{2} \cdot 578 0^{4}

Solution

3.89673 E 26

Solution steps

5.67 \cdot 1 0^{- 8} \cdot 4 π (7 \cdot 1 0^{8})^{2} \cdot 578 0^{4}

Apply exponent rule:

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

= 578 0^{4} \cdot 4 \cdot 5.67 π \frac{1}{1 0 ^{8}} (1 0^{8} \cdot 7)^{2}

(7 \cdot 1 0^{8})^{2} = 1 0^{16} \cdot 7^{2}

= 1 0^{16} \cdot 578 0^{4} \cdot 7^{2} \cdot 4 \cdot 5.67 π \frac{1}{1 0 ^{8}}

Factor integer

4 = 2^{2}

= 5.67 \cdot \frac{1}{1 0 ^{8}} \cdot 2^{2} π 7^{2} \cdot 1 0^{16} \cdot 578 0^{4}

Factor integer

10 = 2 \cdot 5

= 5.67 \cdot \frac{1}{1 0 ^{8}} \cdot 2^{2} π 7^{2} (2 \cdot 5)^{16} \cdot 578 0^{4}

Apply exponent rule:

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

(2 \cdot 5)^{16} = 2^{16} \cdot 5^{16}

= 5.67 \cdot \frac{1}{1 0 ^{8}} \cdot 2^{2} π 7^{2} \cdot 2^{16} \cdot 5^{16} \cdot 578 0^{4}

Factor integer

5780 = 2^{2} \cdot 5 \cdot 289

= 5.67 \cdot \frac{1}{1 0 ^{8}} \cdot 2^{2} π 7^{2} \cdot 2^{16} \cdot 5^{16} (2^{2} \cdot 5 \cdot 289)^{4}

Apply exponent rule:

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

(2^{2} \cdot 5 \cdot 289)^{4} = (2^{2})^{4} \cdot 5^{4} \cdot 28 9^{4}

= 5.67 \cdot \frac{1}{1 0 ^{8}} \cdot 2^{2} π 7^{2} \cdot 2^{16} \cdot 5^{16} (2^{2})^{4} \cdot 5^{4} \cdot 28 9^{4}

Apply exponent rule:

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

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

= 5.67 \cdot \frac{1}{1 0 ^{8}} \cdot 2^{2} π 7^{2} \cdot 2^{16} \cdot 5^{16} \cdot 2^{2 \cdot 4} \cdot 5^{4} \cdot 28 9^{4}

Refine

= 5.67 \cdot \frac{1}{1 0 ^{8}} \cdot 2^{2} π 7^{2} \cdot 2^{16} \cdot 5^{16} \cdot 2^{8} \cdot 5^{4} \cdot 28 9^{4}

Apply exponent rule:

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

2^{2} \cdot 2^{16} \cdot 2^{8} = 2^{2 + 16 + 8}

= 5.67 \cdot \frac{1}{1 0 ^{8}} π 7^{2} \cdot 5^{16} \cdot 2^{2 + 16 + 8} \cdot 5^{4} \cdot 28 9^{4}

Add the numbers:

2 + 16 + 8 = 26

= 5.67 \cdot \frac{1}{1 0 ^{8}} π 7^{2} \cdot 5^{16} \cdot 2^{26} \cdot 5^{4} \cdot 28 9^{4}

Apply exponent rule:

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

5^{16} \cdot 5^{4} = 5^{16 + 4}

= 5.67 \cdot \frac{1}{1 0 ^{8}} π 7^{2} \cdot 2^{26} \cdot 5^{16 + 4} \cdot 28 9^{4}

Add the numbers:

16 + 4 = 20

= 5.67 \cdot \frac{1}{1 0 ^{8}} π 7^{2} \cdot 2^{26} \cdot 5^{20} \cdot 28 9^{4}

Multiply fractions:

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

= 5.67 \cdot \frac{2 ^{26} \cdot 5 ^{20} \cdot 28 9 ^{4} \cdot 7 ^{2} \cdot 1 π}{1 0 ^{8}}

\frac{1 π 7 ^{2} \cdot 2 ^{26} \cdot 5 ^{20} \cdot 28 9 ^{4}}{1 0 ^{8}} = 28 9^{4} \cdot 3.136 E 15 π

= 28 9^{4} \cdot 3.136 E 15 \cdot 5.67 π

Multiply the numbers:

5.67 \cdot 3.136 E 15 = 1.77811 E 16

= 28 9^{4} \cdot 1.77811 E 16 π

Convert element to a decimal form

28 9^{4} = 6975757441

= 1.77811 E 16 \cdot 6975757441 π

Multiply the numbers:

1.77811 E 16 \cdot 6975757441 \cdot 3.14159 \dots = 3.89673 E 26

= 3.89673 E 26

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Frequently Asked Questions (FAQ)

What is 5.67*10^{-8}*4pi(7*10^8)^2*5780^4 ?
The solution to 5.67*10^{-8}*4pi(7*10^8)^2*5780^4 is 3.89673E26

simplify 5.67*10^{-8}*4pi(7*10^8)^2*5780^4

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 5.67*10^{-8}*4pi(7*10^8)^2*5780^4 ?

simplify 5.6710^{-8}4pi(710^8)^25780^4

What is 5.6710^{-8}4pi(710^8)^25780^4 ?