These videos will take you through the solutions of several kinds of problems you might encounter using rational and negative exponents, alone or in combinations.
Here are three whole numbers raised to rational powers to give you an idea of how these can be simplified exactly and pretty quickly without a calculator. You just need to know the laws of exponents (and remember the multiplication table). The last example shows you how to solve a problem like xa/b = 25, by raising both sides to the b/a power.
Here are two more examples, the first like the last on the previous video, only with a negative rational exponent on x. The second example is of the kind you'll encounter often: a ratio of several variables raised to various rational and negative powers. One strategy (used here) is to deal with the negative exponents first, by moving them across the division line and dropping the negative sign.
Here are two more examples of simplifying ratios of variables raised to rational and negative powers.
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