How do you evaluate #7.1\times 10^ { - 4} \times 6.7\times 10^ { 8}#?

1 Answer
smendyka
Nov 21, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

#(7.1 xx 6.7) xx (10^-4 xx 10^8) =>#

#47.57 xx (10^-4 xx 10^8)#

Next, use this rule for exponents to multiply the 10s terms:

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

#47.57(10^color(red)(-4) xx 10^color(blue)(8)) =>#

#47.57 xx 10^(color(red)(-4) + color(blue)(8)) =>#

#47.57 xx 10^4#

If you need to put the expression into Scientific Notation we need to move the decimal point 1 place to the left so we need to add #1# to the exponent for the 10s term:

#4.757 xx 10^5#

If you need to write this as a number we can move the decimal point 5 places to the right giving:

#475,700#

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