Download Rational (Fractional) Exponent Equations

Rational (Fractional) Exponent Equations
Remember that a fractional exponent can be written in radical form.
3
x
2
( )
= x 3 or
3
x
2
x
3
= 3 x 2 or
( )
3
x
2
2
x
5
= 5 x 2 or
( )
5
2
x
The denominator of the fraction becomes the index of the radical. In other
words, it tells us what root to take. The numerator becomes the power of the
expression.
If you encounter an equation that has a variable raised to a fractional
exponent, you solve it just like a radical equation.
Process:
1. Isolate the expression with the variable.
2. Get rid of the exponent on the expression with the variable by
raising both sides to the appropriate power.
3. Solve the resulting equation.
4. Check for extraneous solutions.
(x
2
+ 6x − 7)
3
2
= 27
( 3x
2
− 11x + 10 )
2
( x − 2) 3 = 9
3
2
=8
2
( x + 5) 5 = 9
3
( 5x − 4) 4 = 8