What is (6.67*10^{-11})(5*10^2)(8*10^{20}) ?

The solution to (6.67*10^{-11})(5*10^2)(8*10^{20}) is 2.668E13

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simplify (6.6710^{-11})(510^2)(8*10^{20})

simplify

(6.67 \cdot 1 0^{- 11}) (5 \cdot 1 0^{2}) (8 \cdot 1 0^{20})

2.668 E 13

Solution steps

(6.67 \cdot 1 0^{- 11}) (5 \cdot 1 0^{2}) (8 \cdot 1 0^{20})

Apply exponent rule:

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

= 1 0^{20} \cdot 1 0^{2} \cdot 5 \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 5 (2 \cdot 5)^{2} \cdot 8 \cdot 1 0^{20}

Apply exponent rule:

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

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

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 5 \cdot 2^{2} \cdot 5^{2} \cdot 8 \cdot 1 0^{20}

Factor integer

8 = 2^{3}

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 5 \cdot 2^{2} \cdot 5^{2} \cdot 2^{3} \cdot 1 0^{20}

Factor integer

10 = 2 \cdot 5

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 5 \cdot 2^{2} \cdot 5^{2} \cdot 2^{3} (2 \cdot 5)^{20}

Apply exponent rule:

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

(2 \cdot 5)^{20} = 2^{20} \cdot 5^{20}

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 5 \cdot 2^{2} \cdot 5^{2} \cdot 2^{3} \cdot 2^{20} \cdot 5^{20}

Apply exponent rule:

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

2^{2} \cdot 2^{3} \cdot 2^{20} = 2^{2 + 3 + 20}

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 5 \cdot 5^{2} \cdot 2^{2 + 3 + 20} \cdot 5^{20}

Add the numbers:

2 + 3 + 20 = 25

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 5 \cdot 5^{2} \cdot 2^{25} \cdot 5^{20}

Apply exponent rule:

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

5 \cdot 5^{2} \cdot 5^{20} = 5^{1 + 2 + 20}

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 2^{25} \cdot 5^{1 + 2 + 20}

Add the numbers:

1 + 2 + 20 = 23

= 6.67 \cdot \frac{1}{1 0 ^{11}} \cdot 2^{25} \cdot 5^{23}

Multiply fractions:

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

= 6.67 \cdot \frac{2 ^{25} \cdot 5 ^{23} \cdot 1}{1 0 ^{11}}

\frac{1 \cdot 2 ^{25} \cdot 5 ^{23}}{1 0 ^{11}} = 4000000000000

= 4000000000000 \cdot 6.67

Multiply the numbers:

6.67 \cdot 4000000000000 = 2.668 E 13

= 2.668 E 13

A (x - 2) e^{- x}

- 1600 e^{- \frac{0}{100}}

\frac{a - b \cdot a + b}{( a - b ) \cdot a ^{2} - b ^{2}}

0.06 (1149) \cdot (1 + 0.0015 \cdot 1149)^{- \frac{1}{2}}

0.0000564 \cdot 1 0^{- 3}

What is (6.67*10^{-11})(5*10^2)(8*10^{20}) ?
The solution to (6.67*10^{-11})(5*10^2)(8*10^{20}) is 2.668E13