I need help simplifying a rational expression.

Need help simplifying this expression?

• Using the law of exponents would (2a)^5 / a^-2 = 2^5*a^7 I figured I could factor it out to be 2^5 * a^5 / a^-2 Thinking that I could just take the inverse of a^-2 and add it to the top line.. hence getting 2^5 * a^5 * a^2 simplified to 2^5*a^7 But when I look at the quotient laws a^b/a^c = a^b-c it would it equal 2a^7 Plugging in a number for the variable I get 2 different answers for each. If I am wrong on both counts then let me know.

• Answer:

  How did you come up with 2a^7 ? You've applied a^b/a^c = a^b-c incorrectly. What you have is a slightly different case: (a*d)^b/a^c (a*d)^b = a^b * d^b Therefore: (a*d)^b/a^c = (a^b * d^b)/a^c=d^b * (a^b /a^c) = d^b * a^(b-c). So the correct answer is of course "2^5*a^7" - i.e. your first answer was spot on!