properties of exponents

[megadeth95]

Hello, i need help with the foll. problems:

1. (2m²)^-1 / m²

2. (2hjk)⁰ / 2h^-3j^-4k^-2

this is what i did so far

1. (2m²)^-1 / m² = (2^-1 * m^-2) / m²

= m²/2*m²

= 1/2



2. (2hjk)⁰ / 2h^-3j^-4k^-2 = 1/ 2h^-3j^-4k^-2


= 2 / h³j⁴k²

Is this correct?? thanks in advance!

 

[megadeth95]

for the first problem:

(2m²)^-1 / m²

= (2^-1 * m^-2) / m²

= (1/ 2¹ * 1/m²) / m²

= (1/ 2m²) / m²

= 1/ 2m⁴

for the second one:

(2hjk)⁰ / 2h^-3j^-4k^-2

= 1 / 2h^-3j^-4k^-2

= 1 / 2(1/h³ * 1/j⁴ * k ² )

= 1 / (2/h³j⁴k²)

= h³j⁴k² / 2

 

[megadeth95]

For the first one, you need to remember that you can always turn a number into a fraction So \(\displaystyle n = \dfrac{n}{1}\)

You also need to remember how to divide fractions

\(\displaystyle \dfrac{\dfrac{a}{b}}{\dfrac{c}{d}} = \dfrac{a}{b} * \dfrac{d}{c} = \dfrac{ad}{bc}\)

So \(\displaystyle \dfrac{\dfrac{1}{2} * \dfrac{1}{m^2}}{m^2} =\) \(\displaystyle \dfrac{\dfrac{1}{2m^2}}{\dfrac{m^2}{1}} =\) \(\displaystyle \dfrac{1}{2m^2} * \dfrac{1}{m^2} = \dfrac{1}{2m^4}\)

ohh.... it was really easy, a piece of cake. I really need to remember the old lessons about dividing fractions! thank you very much!! you helped me a lot

 

[lookagain]

Hello, i need help with the foll. problems:

1. (2m²)^-1 / m²

2. (2hjk)⁰ /( 2h^-3j^-4k)



this is what i did so far


1. (2m²)^-1 / m² = (2^-1 * m^-2) / m²

= m²/(2*m² )

= 1/2



2. \(\displaystyle (2hjk)^0 /(2h^{-3}j^{-4}k^{-2}) \)


\(\displaystyle = 1/(2h^{-3}j^{-4}k^{-2})\)


= \(\displaystyle 1/(2h^{-3}j^{-4}k^{-2})\)


\(\displaystyle 2/(h^3j^4k^2)\)

Is this correct?? thanks in advance!

megadeth95,

aside from your steps being correct or not, certain of your denominators
must have grouping symbols because of the Order of Operations.

I made some suggested changes above. However, I did not correct
steps regarding to the proper values of the exponents, or even if
you had the correct forms of fractions.