How do you evaluate #4\times 10^ { - 7} \times 1\times 10^ { - 3}#?

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Answer 1 · 2017-06-18T19:50:04

See a solution process below:

First, rewrite the expression as:

#(4 xx 1) xx (10^-7 xx 10^-3) => 4 xx (10^-7 xx 10^-3)#

Now, use this rule for exponents to evaluate the product of 10s terms:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#4 xx (10^color(red)(-7) xx 10^color(blue)(-3)) = 4xx 10^(color(red)(-7) + color(blue)(-3)) => 4 xx 10^-10#

If we wanted to write this in standard notation we would need to move the decimal point 10 places to the left:

#4 xx 10^-10 = 0.0000000004#

Answer 2 · 2017-06-18T21:07:19

#0.0000000004#

We have: #4 times 10^(- 7) times 1 times 10^(- 3)#

#= 4 times 10^(- 7) times 10^(- 3)#

Using the laws of exponents:

#= 4 times 10^(- 7 + (- 3))#

#= 4 times 10^(- 10)#

#= 4 times frac(1)(10^(10))#

#= frac(4)(10^(10))#

#= 0.0000000004#