How to solve Fraction Exponents $x ^{\frac{2}{3}} +1 = 65$

Exponential Equations with a radical in the exponent

Before you attempt to solve exponential equations with radical exponents (ie fraction exponents) you should be comfortable

How To Solve Fraction Exponents (Steps)

• Isolate the expression with the fractional exponent
• raise both sides to the reciprocal of the exponent
• simplify

Example

$x ^{\frac{2}{3}} +1 = 65$ Step 1

Isolate fraction exponent

Step 2

Raise both sides to reciprocal of exponent

Step 2

Simplify x = 512