What is (86400^2)(6.673*10^{-11})(5.974*10^{24}) ?

The solution to (86400^2)(6.673*10^{-11})(5.974*10^{24}) is 2.97587E24

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simplify (86400^2)(6.67310^{-11})(5.97410^{24})

Solution

simplify

(8640 0^{2}) (6.673 \cdot 1 0^{- 11}) (5.974 \cdot 1 0^{24})

Solution

2.97587 E 24

Solution steps

(8640 0^{2}) (6.673 \cdot 1 0^{- 11}) (5.974 \cdot 1 0^{24})

Apply exponent rule:

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

= 1 0^{24} \cdot 8640 0^{2} \cdot 5.974 \cdot 6.673 \cdot \frac{1}{1 0 ^{11}}

Factor integer

86400 = 2^{7} \cdot 5^{2} \cdot 27

= (2^{7} \cdot 5^{2} \cdot 27)^{2} \cdot 6.673 \cdot \frac{1}{1 0 ^{11}} \cdot 5.974 \cdot 1 0^{24}

Apply exponent rule:

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

(2^{7} \cdot 5^{2} \cdot 27)^{2} = (2^{7})^{2} (5^{2})^{2} \cdot 2 7^{2}

= (2^{7})^{2} (5^{2})^{2} \cdot 2 7^{2} \cdot 6.673 \cdot \frac{1}{1 0 ^{11}} \cdot 5.974 \cdot 1 0^{24}

Apply exponent rule:

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

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

= 2^{7 \cdot 2} \cdot 5^{2 \cdot 2} \cdot 2 7^{2} \cdot 6.673 \cdot \frac{1}{1 0 ^{11}} \cdot 5.974 \cdot 1 0^{24}

Refine

= 2^{14} \cdot 5^{4} \cdot 2 7^{2} \cdot 6.673 \cdot \frac{1}{1 0 ^{11}} \cdot 5.974 \cdot 1 0^{24}

Factor integer

10 = 2 \cdot 5

= 2^{14} \cdot 5^{4} \cdot 2 7^{2} \cdot 6.673 \cdot \frac{1}{1 0 ^{11}} \cdot 5.974 (2 \cdot 5)^{24}

Apply exponent rule:

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

(2 \cdot 5)^{24} = 2^{24} \cdot 5^{24}

= 2^{14} \cdot 5^{4} \cdot 2 7^{2} \cdot 6.673 \cdot \frac{1}{1 0 ^{11}} \cdot 5.974 \cdot 2^{24} \cdot 5^{24}

Apply exponent rule:

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

2^{14} \cdot 2^{24} = 2^{14 + 24}

= 5^{4} \cdot 2 7^{2} \cdot 6.673 \cdot \frac{1}{1 0 ^{11}} \cdot 5.974 \cdot 2^{14 + 24} \cdot 5^{24}

Add the numbers:

14 + 24 = 38

= 5^{4} \cdot 2 7^{2} \cdot 6.673 \cdot \frac{1}{1 0 ^{11}} \cdot 5.974 \cdot 2^{38} \cdot 5^{24}

Apply exponent rule:

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

5^{4} \cdot 5^{24} = 5^{4 + 24}

= 2 7^{2} \cdot 6.673 \cdot \frac{1}{1 0 ^{11}} \cdot 5.974 \cdot 2^{38} \cdot 5^{4 + 24}

Add the numbers:

4 + 24 = 28

= 2 7^{2} \cdot 6.673 \cdot \frac{1}{1 0 ^{11}} \cdot 5.974 \cdot 2^{38} \cdot 5^{28}

Multiply fractions:

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

= 5.974 \cdot 6.673 \cdot \frac{2 ^{38} \cdot 5 ^{28} \cdot 2 7 ^{2} \cdot 1}{1 0 ^{11}}

\frac{1 \cdot 2 7 ^{2} \cdot 2 ^{38} \cdot 5 ^{28}}{1 0 ^{11}} = 5^{17} \cdot 97844723712

= 5^{17} \cdot 97844723712 \cdot 5.974 \cdot 6.673

Multiply the numbers:

6.673 \cdot 5.974 \cdot 97844723712 = 3900531184106.471

= 5^{17} \cdot 3900531184106.471

Convert element to a decimal form

5^{17} = 762939453125

= 762939453125 \cdot 3900531184106.471

Multiply the numbers:

3900531184106.471 \cdot 762939453125 = 2.97587 E 24

= 2.97587 E 24

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Frequently Asked Questions (FAQ)

What is (86400^2)(6.673*10^{-11})(5.974*10^{24}) ?
The solution to (86400^2)(6.673*10^{-11})(5.974*10^{24}) is 2.97587E24

simplify (86400^2)(6.673*10^{-11})(5.974*10^{24})

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is (86400^2)(6.673*10^{-11})(5.974*10^{24}) ?

simplify (86400^2)(6.67310^{-11})(5.97410^{24})

What is (86400^2)(6.67310^{-11})(5.97410^{24}) ?