Question #1bb1d

1 Answer
Dec 20, 2017

Answer:

See a solution process below:

Explanation:

First, excluded values would be when the denominator is equal to #0# or:

#10h^2z^3 = 0# or when #h = 0# or #z = 0#

First, rewrite the expression as:

#(3 xx 2)/(5 xx 2)(h^3/h^2)(z/z^3) =>#

#(3 xx color(red)(cancel(color(black)(2))))/(5 xx color(red)(cancel(color(black)(2))))(h^3/h^2)(z/z^3) =>#

#3/5(h^3/h^2)(z/z^3)#

Next, use these rules of exponents to simplify the #h# terms:

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

#3/5(h^color(red)(3)/h^color(blue)(2))(z/z^3) =>#

#3/5(h^(color(red)(3)-color(blue)(2)))(z/z^3) =>#

#3/5(h^1)(z/z^3) =>#

#3/5(h)(z/z^3) =>#

#(3h)/5(z/z^3)#

Now, use these rules of exponents to simplify the #z# term:

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

#(3h)/5(z/z^3) =>#

#(3h)/5(z^color(red)(1)/z^color(blue)(3)) =>#

#(3h)/5(1/z^(color(blue)(3)-color(red)(1))) =>#

#(3h)/5(1/z^2) =>#

#(3h)/(5z^2)#