For example, you can rewrite
asFractional exponents are roots and nothing else. For example, 641/3 doesn’t mean 64–3 or
In this example, you find the root shown in the denominator (the cube root) and then take it to the power in the numerator (the first power). So 641/3 = 4.
The order of these processes really doesn’t matter. You can choose either method:
Cube root the 8 and then square that product
Square the 8 and then cube root that product
Take a look at some steps that illustrate this process. To simplify the expression
rather than work with the roots, execute the following:
Rewrite the entire expression using rational exponents.
Now you have all the properties of exponents available to help you to simplify the expression: x1/2(x2/3 – x4/3).
Distribute to get rid of the parentheses.
When you multiply monomials with the same base, you add the exponents.
Hence, the exponent on the first term is
and the exponent of the second term is 1/2+4/3=11/6. So you get x7/6 – x11/6.
Because the solution is written in exponential form and not in radical form, as the original expression was, rewrite it to match the original expression.
This gives you