What is (6.67*10^{-11})(6*10^7)(6*10^7) ?

The solution to (6.67*10^{-11})(6*10^7)(6*10^7) is 240120

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simplify (6.6710^{-11})(610^7)(6*10^7)

Solution

simplify

(6.67 \cdot 1 0^{- 11}) (6 \cdot 1 0^{7}) (6 \cdot 1 0^{7})

Solution

240120

Solution steps

(6.67 \cdot 1 0^{- 11}) (6 \cdot 1 0^{7}) (6 \cdot 1 0^{7})

Apply exponent rule:

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

6 \cdot 6 = 6^{1 + 1}

= 6.67 \cdot 1 0^{- 11} \cdot 1 0^{7} \cdot 6^{1 + 1} \cdot 1 0^{7}

Add the numbers:

1 + 1 = 2

= 6.67 \cdot 1 0^{- 11} \cdot 1 0^{7} \cdot 6^{2} \cdot 1 0^{7}

Factor integer

10 = 2 \cdot 5

= 6.67 (2 \cdot 5)^{- 11} \cdot 1 0^{7} \cdot 6^{2} \cdot 1 0^{7}

Apply exponent rule:

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

(2 \cdot 5)^{- 11} = 2^{- 11} \cdot 5^{- 11}

= 6.67 \cdot 2^{- 11} \cdot 5^{- 11} \cdot 1 0^{7} \cdot 6^{2} \cdot 1 0^{7}

Factor integer

10 = 2 \cdot 5

= 6.67 \cdot 2^{- 11} \cdot 5^{- 11} (2 \cdot 5)^{7} \cdot 6^{2} \cdot 1 0^{7}

Apply exponent rule:

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

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

= 6.67 \cdot 2^{- 11} \cdot 5^{- 11} \cdot 2^{7} \cdot 5^{7} \cdot 6^{2} \cdot 1 0^{7}

Factor integer

6 = 2 \cdot 3

= 6.67 \cdot 2^{- 11} \cdot 5^{- 11} \cdot 2^{7} \cdot 5^{7} (2 \cdot 3)^{2} \cdot 1 0^{7}

Apply exponent rule:

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

(2 \cdot 3)^{2} = 2^{2} \cdot 3^{2}

= 6.67 \cdot 2^{- 11} \cdot 5^{- 11} \cdot 2^{7} \cdot 5^{7} \cdot 2^{2} \cdot 3^{2} \cdot 1 0^{7}

Factor integer

10 = 2 \cdot 5

= 6.67 \cdot 2^{- 11} \cdot 5^{- 11} \cdot 2^{7} \cdot 5^{7} \cdot 2^{2} \cdot 3^{2} (2 \cdot 5)^{7}

Apply exponent rule:

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

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

= 6.67 \cdot 2^{- 11} \cdot 5^{- 11} \cdot 2^{7} \cdot 5^{7} \cdot 2^{2} \cdot 3^{2} \cdot 2^{7} \cdot 5^{7}

Apply exponent rule:

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

2^{- 11} \cdot 2^{7} \cdot 2^{2} \cdot 2^{7} = 2^{- 11 + 7 + 2 + 7}

= 6.67 \cdot 5^{- 11} \cdot 5^{7} \cdot 3^{2} \cdot 2^{- 11 + 7 + 2 + 7} \cdot 5^{7}

Add/Subtract the numbers:

- 11 + 7 + 2 + 7 = 5

= 6.67 \cdot 5^{- 11} \cdot 5^{7} \cdot 3^{2} \cdot 2^{5} \cdot 5^{7}

Apply exponent rule:

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

5^{- 11} \cdot 5^{7} \cdot 5^{7} = 5^{- 11 + 7 + 7}

= 6.67 \cdot 3^{2} \cdot 2^{5} \cdot 5^{- 11 + 7 + 7}

Add/Subtract the numbers:

- 11 + 7 + 7 = 3

= 6.67 \cdot 3^{2} \cdot 2^{5} \cdot 5^{3}

3^{2} = 9

= 2^{5} \cdot 5^{3} \cdot 9 \cdot 6.67

2^{5} = 32

= 5^{3} \cdot 9 \cdot 32 \cdot 6.67

5^{3} = 125

= 9 \cdot 32 \cdot 125 \cdot 6.67

Multiply the numbers:

6.67 \cdot 9 \cdot 32 \cdot 125 = 240120

= 240120

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Frequently Asked Questions (FAQ)

What is (6.67*10^{-11})(6*10^7)(6*10^7) ?
The solution to (6.67*10^{-11})(6*10^7)(6*10^7) is 240120

simplify (6.67*10^{-11})(6*10^7)(6*10^7)

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is (6.67*10^{-11})(6*10^7)(6*10^7) ?

simplify (6.6710^{-11})(610^7)(6*10^7)

What is (6.6710^{-11})(610^7)(6*10^7) ?