How do you simplify #(64qt)/(16q^2t^3)# and find the excluded values?

1 Answer
Nov 5, 2017

Answer:

See a solution process below:

Explanation:

To simplify this expression, first rewrite the expression as:

#64/16(q/q^2)(t/t^3) =>#

#4(q/q^2)(t/t^3)#

Next, use this rule of exponents to rewrite the expression:

#a = a^color(red)(1)#

#4(q^color(red)(1)/q^2)(t^color(red)(1)/t^3)#

Now, use this rule for exponents to simplify the #q# and #t# terms:

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

#4(q^color(red)(1)/q^color(blue)(2))(t^color(red)(1)/t^color(blue)(3)) =>#

#4(1/q^(color(blue)(2)-color(red)(1)))(1/t^(color(blue)(3)-color(red)(1))) =>#

#4(1/q^1)(1/t^2) =>#

#4(1/q)(1/t^2) =>#

#4/(qt^2)#

To find the exclude values for this expression we need to equate the denominator of the original expression to #0# and solve for each term equal to #0#:

#16q^2t^3 = 0#

First Excluded Value:

#q^2 = 0#

#q = 0#

Second Excluded Value:

#t^3 = 0#

#t = 0#

The Excluded Values Are: #q = 0# and/or #t = 0#