What is (6.7*10^{-11})(2*10^{24})(8*10^{30}) ?

The solution to (6.7*10^{-11})(2*10^{24})(8*10^{30}) is 1.072E45

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simplify (6.710^{-11})(210^{24})(8*10^{30})

Solution

simplify

(6.7 \cdot 1 0^{- 11}) (2 \cdot 1 0^{24}) (8 \cdot 1 0^{30})

Solution

1.072 E 45

Solution steps

(6.7 \cdot 1 0^{- 11}) (2 \cdot 1 0^{24}) (8 \cdot 1 0^{30})

Apply exponent rule:

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

= 1 0^{30} \cdot 1 0^{24} \cdot 2 \cdot 8 \cdot 6.7 \cdot \frac{1}{1 0 ^{11}}

Factor integer

10 = 2 \cdot 5

= 6.7 \cdot \frac{1}{1 0 ^{11}} \cdot 2 (2 \cdot 5)^{24} \cdot 8 \cdot 1 0^{30}

Apply exponent rule:

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

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

= 6.7 \cdot \frac{1}{1 0 ^{11}} \cdot 2 \cdot 2^{24} \cdot 5^{24} \cdot 8 \cdot 1 0^{30}

Factor integer

8 = 2^{3}

= 6.7 \cdot \frac{1}{1 0 ^{11}} \cdot 2 \cdot 2^{24} \cdot 5^{24} \cdot 2^{3} \cdot 1 0^{30}

Factor integer

10 = 2 \cdot 5

= 6.7 \cdot \frac{1}{1 0 ^{11}} \cdot 2 \cdot 2^{24} \cdot 5^{24} \cdot 2^{3} (2 \cdot 5)^{30}

Apply exponent rule:

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

(2 \cdot 5)^{30} = 2^{30} \cdot 5^{30}

= 6.7 \cdot \frac{1}{1 0 ^{11}} \cdot 2 \cdot 2^{24} \cdot 5^{24} \cdot 2^{3} \cdot 2^{30} \cdot 5^{30}

Apply exponent rule:

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

2 \cdot 2^{24} \cdot 2^{3} \cdot 2^{30} = 2^{1 + 24 + 3 + 30}

= 6.7 \cdot \frac{1}{1 0 ^{11}} \cdot 5^{24} \cdot 2^{1 + 24 + 3 + 30} \cdot 5^{30}

Add the numbers:

1 + 24 + 3 + 30 = 58

= 6.7 \cdot \frac{1}{1 0 ^{11}} \cdot 5^{24} \cdot 2^{58} \cdot 5^{30}

Apply exponent rule:

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

5^{24} \cdot 5^{30} = 5^{24 + 30}

= 6.7 \cdot \frac{1}{1 0 ^{11}} \cdot 2^{58} \cdot 5^{24 + 30}

Add the numbers:

24 + 30 = 54

= 6.7 \cdot \frac{1}{1 0 ^{11}} \cdot 2^{58} \cdot 5^{54}

Multiply fractions:

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

= 6.7 \cdot \frac{2 ^{58} \cdot 5 ^{54} \cdot 1}{1 0 ^{11}}

\frac{1 \cdot 2 ^{58} \cdot 5 ^{54}}{1 0 ^{11}} = 2^{47} \cdot 5^{43}

= 2^{47} \cdot 5^{43} \cdot 6.7

Convert element to a decimal form

2^{47} = 1.40737 E 14

= 5^{43} \cdot 1.40737 E 14 \cdot 6.7

Convert element to a decimal form

5^{43} = 1.13687 E 30

= 1.40737 E 14 \cdot 6.7 \cdot 1.13687 E 30

Multiply the numbers:

6.7 \cdot 1.40737 E 14 \cdot 1.13687 E 30 = 1.072 E 45

= 1.072 E 45

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Frequently Asked Questions (FAQ)

What is (6.7*10^{-11})(2*10^{24})(8*10^{30}) ?
The solution to (6.7*10^{-11})(2*10^{24})(8*10^{30}) is 1.072E45

simplify (6.7*10^{-11})(2*10^{24})(8*10^{30})

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is (6.7*10^{-11})(2*10^{24})(8*10^{30}) ?

simplify (6.710^{-11})(210^{24})(8*10^{30})

What is (6.710^{-11})(210^{24})(8*10^{30}) ?