What is (4.2x10^6)(2x10^{-4}) ?

The solution to (4.2x10^6)(2x10^{-4}) is 840x^2

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simplify (4.2x10^6)(2x10^{-4})

simplify

(4.2 x 1 0^{6}) (2 x 1 0^{- 4})

840 x^{2}

Solution steps

(4.2 x \cdot 1 0^{6}) (2 x \cdot 1 0^{- 4})

Simplify

2 x \cdot 1 0^{- 4} : \frac{x}{5000}

= 4.2 x \cdot 1 0^{6} \cdot \frac{x}{5000}

4.2 = \frac{21}{5}

= \frac{21}{5} x \cdot 1 0^{6} \cdot \frac{x}{5000}

Apply the fraction rule:

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

= \frac{21 x \cdot 1 0 ^{6} x}{5 \cdot 5000}

Multiply the numbers:

5 \cdot 5000 = 25000

= \frac{21 x \cdot 1 0 ^{6} x}{25000}

Apply exponent rule:

aa = a^{2}

xx = x^{2}

= \frac{21 x ^{2} \cdot 1 0 ^{6}}{25000}

Factor

25000 : 1 0^{3} \cdot 25

= \frac{21 x ^{2} \cdot 1 0 ^{6}}{1 0 ^{3} \cdot 25}

\frac{1 0 ^{6}}{1 0 ^{3}} = 1 0^{3}

= \frac{21 x ^{2} \cdot 1 0 ^{3}}{25}

Factor

1 0^{3} : 5^{3} \cdot 2^{3}

= \frac{21 x ^{2} \cdot 5 ^{3} \cdot 2 ^{3}}{25}

Factor the number:

25 = 5^{2}

= \frac{21 x ^{2} \cdot 5 ^{3} \cdot 2 ^{3}}{5 ^{2}}

\frac{5 ^{3}}{5 ^{2}} = 5

= 21 x^{2} \cdot 5 \cdot 2^{3}

Multiply the numbers:

21 \cdot 5 = 105

= 105 x^{2} \cdot 2^{3}

= 2^{3} \cdot 105 x^{2}

2^{3} = 8

= 8 \cdot 105 x^{2}

Multiply the numbers:

8 \cdot 105 = 840

= 840 x^{2}

1.588 \cdot 1 0^{- 1}

e^{3 x} e^{- 2 x}

4^{x} 0. 4^{x}

e^{- (\frac{1}{10})^{2}}