How do I solve this dividing monomials problem?

Question

 m^-2 n^-5 / (m^4 n^3)^-1

 

1. Please explains the steps because I don't understand monomials at all.
2. By the way the carat means the next number is an Exponent. 

Answer 1

(m^-2)(n^-5)/((m⁴)(n³)^-1)

 

you could also notice that the denominator is also to the -1 power which means that it becomes part of the numerator

 

1/x = x^-1

1/x^-1 = x

 

(m^-2)(n^-5)/((m⁴)(n³)^-1) =(m^-2)(n^-5)(m⁴)(n³)= (m^-2)(m⁴)(n^-5)(n³)

 

you can then take your exponents of each variable and add them together

 

(m^-2)(m⁴)(n^-5)(n³) = m^(-2+4)n^(-5+3) = m²n^-2= m²/n²

 

Brad as a side note, you can use the superscript in your editing box to actually show the powers like I did.

 

good luck

Answer 2

Hi again Shelby -- two ideas: "spell out the powers", and minus (-) exponents "flip"

 

m^-2 = 1/(m*m) ... n^-5 = 1/(n*n*n*n*n) ... (m*m*m*m*n*n*n)^-1 = 1/( )

 

mmmm*nnn

mm*nnnnn

 

mm/nn or (m/n)(m/n) or (m/n)^2 ... Best wishes :)