2.9.4 Solving an Equation with Rational Exponents

Question 1

solve an equation

Answer 1

• To solve an equation containing a single rational exponent, isolate the expression with the rational exponent on one side
  of the equation and then raise each side to the reciprocal of that rational exponent.
  • To solve an equation containing two rational exponents (one on each side), raise each side to the LCM (least common
  multiple) of the two rational exponents’ denominators. For example, if the left side is an expression raised to the 1/4 power
  and the right side is an expression raised to the 1/2 power, then raise both sides to the 4th power since 4 is the LCM of the
  two rational exponents’ denominators, 2 and 4.
  • Extraneous solutions do exist for these equations. Always check the possible solutions to determine which, if any, are
  solutions for the equation.