How do you simplify #(12m^-4p^2)/(-15m^3p^-9)#?

3 Answers
Jul 18, 2017

Answer:

See a solution process below:

Explanation:

First, rewrite the expression as:

#(12/-15)(m^-4/m^3)(p^2/p^-9) => -(3 xx 4)/(3 xx 5)(m^-4/m^3)(p^2/p^-9) =>#

#-(color(red)(cancel(color(black)(3))) xx 4)/(color(red)(cancel(color(black)(3))) xx 5)(m^-4/m^3)(p^2/p^-9) =>#

#-4/5(m^-4/m^3)(p^2/p^-9)#

Next, use this rule for exponents to simplify the #m# terms:

#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#

#-4/5(m^color(red)(-4)/m^color(blue)(3))(p^2/p^-9) => -4/5(1/m^(color(blue)(3)-color(red)(-4)))(p^2/p^-9) =>#

#-4/5(1/m^(color(blue)(3)+color(red)(4)))(p^2/p^-9) => -4/5(1/m^7)(p^2/p^-9) =>#

#-4/(5m^7)(p^2/p^-9)#

Now, use this rule for exponents to simplify the #p# terms:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#-4/(5m^7)(p^color(red)(2)/p^color(blue)(-9)) => -4/(5m^7)p^(color(red)(2)-color(blue)(-9)) => -4/(5m^7)p^(color(red)(2)+color(blue)(9)) =>#

#-4/(5m^7)p^11 =>#

#-(4p^11)/(5m^7)#

Jul 18, 2017

Answer:

Factor and divide out common terms

Explanation:

# 12 m^-4p^2 = 3 xx 4 xx 1/m^4 xx p^2#

# 15 m^3 p^-9 = 3xx 5 xx m^3 xx 1/p^9 #

Putting this a complex fraction gives

# { (3 xx 4 xx p^2)/(m^4)}/{(3 xx 5 xx m^3)/(p^9)#

Multiplying both the top and the bottom by the inverse of the bottom gives

# { (3 xx 4 xx p^2) xx (p^9)} / {(m^4) xx( 3 xx 5 xx m^3)}#

dividing out common terms and combining common terms gives

# ( 4 xx p^11)/( 5 xx m^7)#

Jul 18, 2017

Answer:

#(4p^11)/(-5m^7)#

Explanation:

#(12m^-4p^2)/(-15m^3p^-9)#

#:.=(cancel12^4p^(2+9))/(cancel(-15)^-5m^(3+4))#

#:.=(4p^11)/(-5m^7)#