How do you evaluate \frac { ( 3.00\times 10^ { 6} ) ( 2.0\times 10^ { - 3} ) } { 5.0\times 10^ { - 2} }?

2 Answers
smendyka · Stefan V.
Dec 10, 2016

120,000 or 1.2 xx 10^5

Explanation:

First, rearrange the terms in the numerator:

(3.00 xx 2.0 xx 10^6 xx 10^-3)/(5.00 xx 10^-2)

Using the rule for exponents where color(red)(x^a xx x^b = x^(a+b)) we can simplify the numerator to:

(6.00 xx 10^(6-3))/(5.0 xx 10^-2)

(6.00 xx 10^3)/(5.0 xx 10^-2)

Now using the rule for exponents where color(red)(x^a/x^b = x^(a-b)) we can simplify the fraction to:

(6.00 xx 10^((3 - -2)))/5.0

(6.00 xx 10^5)/5.00

Expanding the numerator gives us:

600000/5

120000

Or in scientific notation form:

1.2 xx 10^5

LM
Dec 10, 2016

1.2 * 10^5

Explanation:

((3.00 * 10^6)(2.0 * 10^-3))/(5.0 * 10^-2

multiply out brackets:

(6.0 * 10^3)/(5.0 * 10^-2)

divide 6 by 5:

(1.2 * 10^3)/10^-2

and then the powers of 10:

1.2 * 10^5

(reason:) law of indices:
(a^m/a^n = a^(m-n))

1.2 is between 1 and 10, so we do not need to change this or the power of 10.

final answer: 1.2 * 10^5

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