Question #70369

1 Answer
Jun 17, 2017

Answer:

See a solution process below:

Explanation:

We can use this rule for exponents to rewrite this expression:

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

Substituting the exponents from the problem gives:

#x^color(red)(1-a)/x^color(blue)(a) = x^(color(red)(1-a)-color(blue)(a)) = x^(color(red)(1-1a)-color(blue)(1a)) = x^(1-2a)#

Depending on the value of #a# this may result in a negative exponent. If we want an answer with just positive exponents we can also rewrite this expression using this rule of exponents:

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

Again, substituting the exponents from the problem gives:

#x^color(red)(1 - a)/x^color(blue)(a) = 1/x^(color(blue)(a)-color(red)((1-a))) => 1/x^(color(blue)(a)-color(red)(1+a)) => 1/x^(color(blue)(1a)-color(red)(1+1a)) =>1/x^(2a - 1)#