To remove the rational exponent, cube both sides of the equation:

Now simplify both sides of the equation:

Remember the denominator of a rational exponent is equivalent to the index of a root.

This should simplify quite nicely.

When it gives us,

.

Let's work through this equation involving exponents one term at a time. The first term we see is , for which we can apply the following property:

So if we plug our values into the formula for the property, we get:

Because . Our next term is , for which we'll need the property:

Using the values for our term, we have:

The third term of the equation is , for which the quickest way to evaluate would be using the following property:

Using the values from our term, this gives us:

The next property we will need to consider for our fourth term is given below:

If we plug in the corresponding values from our term, we get:

Finally, our last term requires knowledge of the following simple property: Any number raised to the power of zero is 1. With this in mind, our last term becomes:

Rewriting the equation with all of the values we've just evaluated, we obtain our final answer:

We begin by factoring out the term to get:

This equation gives our first solution:

Then we check for more solutions:

Therefore our solution is

To remove the fractional exponents, raise both sides to the second power and simplify:

Now solve for :

When dividing two exponents with the same base we subtract the exponents:

Negative exponents are dealt with based on the rule

:

What does an exponent of one-third mean? Consider our expression and raise it to the third power.

Simplifying, we get:

Thus, we are looking for a number that when cubed, we get . Thus, we are discussing the cube root of , or .

When an exponent is raised to the power of another exponent, just multiply the exponents together.

We proceed as follows

Write as a fraction

The denominator of the fraction is a , so it becomes a square root.

Take the square root.

Raise to the power.