What is (6.67*10^{-11})*(1*10^{30})*(8*10^{30}) ?

The solution to (6.67*10^{-11})*(1*10^{30})*(8*10^{30}) is 5.336E50

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simplify (6.6710^{-11})(110^{30})(8*10^{30})

Solution

simplify

(6.67 \cdot 1 0^{- 11}) \cdot (1 \cdot 1 0^{30}) \cdot (8 \cdot 1 0^{30})

Solution

5.336 E 50

Solution steps

(6.67 \cdot 1 0^{- 11}) (1 \cdot 1 0^{30}) (8 \cdot 1 0^{30})

Apply exponent rule:

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

= 1 0^{30} \cdot 1 0^{30} \cdot 1 \cdot 8 \cdot 6.67 \cdot \frac{1}{1 0 ^{11}}

Factor integer

10 = 2 \cdot 5

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 1 \cdot (2 \cdot 5)^{30} \cdot 8 \cdot 1 0^{30}

Apply exponent rule:

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

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

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 1 \cdot 2^{30} \cdot 5^{30} \cdot 8 \cdot 1 0^{30}

Factor integer

8 = 2^{3}

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 1 \cdot 2^{30} \cdot 5^{30} \cdot 2^{3} \cdot 1 0^{30}

Factor integer

10 = 2 \cdot 5

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 1 \cdot 2^{30} \cdot 5^{30} \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}

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 1 \cdot 2^{30} \cdot 5^{30} \cdot 2^{3} \cdot 2^{30} \cdot 5^{30}

Apply exponent rule:

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

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

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 1 \cdot 5^{30} \cdot 2^{30 + 3 + 30} \cdot 5^{30}

Add the numbers:

30 + 3 + 30 = 63

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 1 \cdot 5^{30} \cdot 2^{63} \cdot 5^{30}

Apply exponent rule:

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

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

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 1 \cdot 2^{63} \cdot 5^{30 + 30}

Add the numbers:

30 + 30 = 60

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 1 \cdot 2^{63} \cdot 5^{60}

Multiply fractions:

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

= 1 \cdot 6.67 \cdot \frac{2 ^{63} \cdot 5 ^{60} \cdot 1}{1 0 ^{11}}

\frac{1 \cdot 2 ^{63} \cdot 5 ^{60}}{1 0 ^{11}} = 2^{52} \cdot 5^{49}

= 2^{52} \cdot 5^{49} \cdot 1 \cdot 6.67

Multiply the numbers:

6.67 \cdot 1 = 6.67

= 2^{52} \cdot 5^{49} \cdot 6.67

Convert element to a decimal form

2^{52} = 4.5036 E 15

= 5^{49} \cdot 4.5036 E 15 \cdot 6.67

Convert element to a decimal form

5^{49} = 1.77636 E 34

= 4.5036 E 15 \cdot 6.67 \cdot 1.77636 E 34

Multiply the numbers:

6.67 \cdot 4.5036 E 15 \cdot 1.77636 E 34 = 5.336 E 50

= 5.336 E 50

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Frequently Asked Questions (FAQ)

What is (6.67*10^{-11})*(1*10^{30})*(8*10^{30}) ?
The solution to (6.67*10^{-11})*(1*10^{30})*(8*10^{30}) is 5.336E50

simplify (6.67*10^{-11})*(1*10^{30})*(8*10^{30})

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is (6.67*10^{-11})*(1*10^{30})*(8*10^{30}) ?

simplify (6.6710^{-11})(110^{30})(8*10^{30})

What is (6.6710^{-11})(110^{30})(8*10^{30}) ?