Rational Exponents

Question

Based on what I have told you √a² b⁴=ab², but I have made a mistake. Find a counterexample where this is not true. How do you propose we fix the mistake?

Answer 1

Most algebra text books make the assumption that variables represent positive numbers when dealing with even roots of algebraic expressions. For those that do not do that, then absolute value symbols are required when simplifying a radical expression where the resulting expression could represent a negative value.

In your problem let a = -5 and b = 3.

Then √((-5)²(3)⁴) = |-5| 3². It does not equal -5 (9).

If the problem had been √(a⁴b⁴) then a²b² would be OK as an answer because even if a represents a negative number, a² is still positive.