Algebra Division problem

[m2bma]

Find the following quotient and write your answer without using scientific notation.

(6.3 x 10 third power)(4 x 10 negative fifth power)
__________________________________________ (divided by)

(2.1 x 10 negative 4 power)

I flopped my 4 x 10 neg. 5 pwr. to the bottom of the fraction and moved the 2.1 x 10 neg. 4 pwr. to the top of the fraction. Then I divided each number by 4 x 10 to the 5th pwr. but then I got lost. Please help! Thx!

 

[galactus]

When you multiply exponents you add them.

\(\displaystyle \frac{(6.3X10^{3})(4X10^{-5})}{2.1X10^{4}}\)

=\(\displaystyle \frac{25.2X10^{-2}}{2.1X10^{4}}\)

When you divide exponents you subtract them.

=\(\displaystyle \frac{2.52X10^{-1}}{2.1X10^{4}}\)

=\(\displaystyle 1.2X10^{-5}\)

=.000012

 

[m2bma]

Can you break this down a little bit. How did you get 2.52 x 10 ^-1
and then 10 ^-5? Thanks!

 

[wjm11]

Find the following quotient and write your answer without using scientific notation.

(6.3 x 10 third power)(4 x 10 negative fifth power)
__________________________________________ (divided by)

(2.1 x 10 negative 4 power)

Use the “^” symbol to show exponents, and use the “*” or ( ) to show multiplication:

(6.3*10^3)(4*10^(-5)) / (2.1*10^(-4))

A important thing to recognize/understand is that the coefficients of the “10s” are not tied to them. For example, the 2.1 is not “tied to” 10^(-4). If you want to move numbers with negative exponents to either the numerator or denominator in order to change the sign on the exponent, that’s fine – just don’t move the other number with it. So,

(6.3*10^3)(4*10^(-5)) / (2.1*10^(-4))

= [(6.3)(4)/(2.1)] * [(10^3)(10(-5))/(10^(-4))]; Separate terms with exponents.

= [12]* [(10^3)(10(4))/(10^(5))]; Move exponent terms as desired (though not required).

= [12]* [(10^7)/(10^5)]; Combine/simplify.

= [12]* [10^2]; Subtract denominator exponent from numerator exponent.

= 1.2*10^3; Put into scientific notation.

 

[Denis]

Make your life easier: remove the 6.3 * 4 / 2.1 ; you know it equals 12.

So you're left with:
10^3 * 10^-5 / 10^-4
bring up the 10^-4 by changing the exponent's sign:
10^3 * 10^-5 * 10^4
combine by adding the exponents:
10^(3-5+4) = 10^2 = 100

Multiply that by the removed 12: 100* 12 = 1200 = answer