# Precalculus : Simplify Expressions With Rational Exponents

## Example Questions

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Simplify

Explanation:

.

### Example Question #1 : Simplify Expressions With Rational Exponents

Simplify the expression.

Explanation:

Using the properties of exponents, we can either choose to subtract the exponents of the corresponding bases or rewrite the expression using negative exponents as such:

Here, we combine the terms with corresponding bases by adding the exponents together to get

Placing the x term (since it has a negative exponent) in the denominator will result in the correct answer. It can be shown that simply subtracting the exponents of corresponding bases will result in the same answer.

### Example Question #1 : Simplify Expressions With Rational Exponents

Simplify the expression .

Explanation:

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.

### Example Question #1 : Simplify Expressions With Rational Exponents

What is the value of

Explanation:

Recall that when considering rational exponents, the denominator of the fraction tells us the "root" of the expression.

Thus in this case we are taking the fifth root of .

The fifth root of  is , because .

Thus, we have reduced our expression to

### Example Question #1 : Simplify Expressions With Rational Exponents

Simplify the expression:

Explanation:

Simplify the constants:

Subtract the "x" exponents:

This is how the x moves to the denominator.

Finally subtract the "y" exponents:

### Example Question #6 : Simplify Expressions With Rational Exponents

Solve:

Explanation:

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

Now solve for :

### Example Question #1 : Simplify Expressions With Rational Exponents

Solve:

Explanation:

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

Now simplify both sides of the equation:

### Example Question #1 : Simplify Expressions With Rational Exponents

Simplify and rewrite with positive exponents:

Explanation:

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

Negative exponents are dealt with based on the rule

:

### Example Question #1 : Simplify Expressions With Rational Exponents

Simplify the function:

Explanation:

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

Simplify: