Exercise 55 Page 396

To solve equations with a variable expression raised to a rational exponent, we first want to make sure the variable expression is isolated. Then we can raise each side of the equation to the reciprocal of the rational exponent.

x^{\frac{m}{n}} = k \Leftrightarrow (x^{\frac{m}{n}})^{\frac{n}{m}} = k^{\frac{n}{m}}

Let's try to solve our equation using this method!

Finding the Solutions

We will first isolate the variable expression raised to a rational exponent, and then raise each side of the equation to the power of

\frac{3}{4} .