How do you simplify #(2a^4b^3 )/(a^2b)#?

2 Answers
May 30, 2018

Answer:

See a solution process below:

Explanation:

First, rewrite the expression as:

#2(a^4/a^2)(b^3/b)#

Next, use this rule of exponents to rewrite the denominator of the #b# term:

#x = x^color(blue)(1)#

#2(a^4/a^2)(b^3/b^color(blue)(1))#

Now, use this rule of exponents to simplify the #a# and #b# terms:

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

#2(a^color(red)(4)/a^color(blue)(2))(b^color(red)(3)/b^color(blue)(1)) =>#

#2a^(color(red)(4)-color(blue)(2))b^(color(red)(3)-color(blue)(1)) =>#

#2a^2b^2#

May 30, 2018

Answer:

#2a^2b^2#

Explanation:

Remember that exponents underneath the fraction are the same as negative exponents above the fraction. So this expression is the same as #2a^4b^3a^(-2)b^(-1)#, which one then adds as normal:
#2a^(4-2)b^(3-1)=2a^2b^2#.