What is (0.1*10^{-3})*(3*10^8)^2 ?

The solution to (0.1*10^{-3})*(3*10^8)^2 is 10^{16}*0.0009

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simplify (0.110^{-3})(3*10^8)^2

simplify

(0.1 \cdot 1 0^{- 3}) \cdot (3 \cdot 1 0^{8})^{2}

1 0^{16} \cdot 0.0009

Decimal Notation

9000000000000

Solution steps

(0.1 \cdot 1 0^{- 3}) (3 \cdot 1 0^{8})^{2}

Simplify

0.1 \cdot 1 0^{- 3} : 0.0001

= 0.0001 (3 \cdot 1 0^{8})^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(3 \cdot 1 0^{8})^{2} = 3^{2} (1 0^{8})^{2}

= 0.0001 \cdot 3^{2} (1 0^{8})^{2}

3^{2} = 9

= 0.0001 \cdot 9 (1 0^{8})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

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

= 0.0001 \cdot 9 \cdot 1 0^{8 \cdot 2}

Multiply the numbers:

8 \cdot 2 = 16

= 0.0001 \cdot 9 \cdot 1 0^{16}

Multiply the numbers:

0.0001 \cdot 9 = 0.0009

= 0.0009 \cdot 1 0^{16}

= 1 0^{16} \cdot 0.0009

100000000000 0^{100000000 0^{10}}

e^{\frac{1}{2} - 6 x} \cdot 6 e^{\frac{1}{2} + 6 x}

- e^{- x} \cdot 9 e^{3 x}

e^{- \frac{26}{450}}

7.5 \cdot 1 0^{- 1}

What is (0.1*10^{-3})*(3*10^8)^2 ?
The solution to (0.1*10^{-3})*(3*10^8)^2 is 10^{16}*0.0009