Fractional Exponents - Find the expression's value

by Visitor
(Canada)

Question

I have a question that gets to do with fractional exponents. How do we actually find value of this expression?

Answer

We will solve this question using the formula that relates fractional exponents and roots. This formula is shown below:


It is better to take some time to understand how this formula is derived in this lesson on Fractional Exponent.

Now, looking at the expression, we can simplify each of the term in the expression using this formula:


Here's how we can proceed to do so:


(*Note that 8 = 2 × 2 × 2. So cube root of 8 is 3.
Similarly, -8 = -2 × -2 × -2. So, cube root of -8 is -2.)

Hence, we have:


So, the value is 8.