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## SOLVING EQUATIONS INVOLVING RATIONAL EXPONENTS
(If n is even then we require a ≥ 0.) In other words, in a
rational exponent, the numerator indicates
• To solve First,
isolate the variable. Then, raise both sides of the expression to the
• Although you can raise both sides of an equation to the
same power without changing the solutions, • Remember that whenever you have the even root of a
positive number, we get two answers: one • Do NOT attach a when
working with odd roots. When you take the odd root of a number, you • Make sure that the variable is isolated before raising both sides to the same power. For example,
Solve for x in each of the following equations. First, we will isolate the variable. Next, we will raise both sides to the 3/2 Notice that we are unable to isolate the vari- Setting each factor equal to zero, we obtain OR (for an alternative way) Setting each factor equal to zero, we obtain First, we will isolate the variable. Then we First, we will isolate the variable. Next, we will raise both sides to the 3/5 First, we will factor this expression com- Setting each factor equal to zero, we obtain If we check x = -1 by substituting back into Since we cannot isolate the variable, we will Setting each factor equal to zero, we get Because we raised both sides to an even
Notice that the quantity containing the ra- Notice that although this equation does not Simplifying this last equation we get Notice that we cannot solve this one by fac- Setting each factor equal to zero, we obtain |