How do you simplify #(64qt)/(16q^2t^3)# and find the excluded values?
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See a solution process below:
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#
