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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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Examples

In the following example we start with a square root of a quotient.

Example 1

Simplify each expression. Assume all variables represent positive real numbers.

Solution

 Quotient rule for radicals Rationalize the denominator.
 Quotient rule for radicals Product rule for radicals Simplify. Rationalize the denominator.

Any variable with an exponent that is a multiple of 3 is a perfect cube. For example, a3, b6, c15, and w39 are perfect cubes. Each of these expressions is the cube of a variable with an integral exponent. For any values of the variables we can write

Note that when we find the cube root, the result has one-third of the original exponent.

If the exponent on a variable is a multiple of 4, we have a perfect fourth power; if the exponent is a multiple of 5, we have a perfect fifth power; and so on. In the next example we simplify radicals with an index higher than 2.

Example 2