Algebra II : Fractional Exponents

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : Fractional Exponents

Evaluate the expression.

Possible Answers:

Correct answer:

Explanation:

Remember that fraction exponents are the same as radicals.

A shortcut would be to express the terms as exponents and look for opportunities to cancel.

Either method, we then need to multiply to two terms.

 

Example Question #2 : Fractional Exponents

Convert the exponent to radical notation.

Possible Answers:

Correct answer:

Explanation:

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

Example Question #44 : Basic Single Variable Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #3 : Fractional Exponents

Write the product of  in radical form

Possible Answers:

Correct answer:

Explanation:

This problem relies on the key knowledge that  and that the multiplying terms with exponents requires adding the exponents. Therefore, we can rewrite the expression thusly:

Therefore,  is our final answer.

Example Question #4 : Fractional Exponents

Evaluate the following expression:

Possible Answers:

Correct answer:

Explanation:

or

Example Question #5 : Fractional Exponents

Simplify:

Possible Answers:

Correct answer:

Explanation:

Keep in mind that when you are dividing exponents with the same base, you will want to subtract the exponent found in the denominator from the exponent found in the numerator.

To find the exponent for , subtract the denominator's exponent from the numerator's exponent.

To find the exponent for , subtract the denominator's exponent from the numerator's exponent.

Since the exponent is negative, you will want to put the  in the denominator in order to make it positive.

So then,

Example Question #6 : Fractional Exponents

Find the value of .

Possible Answers:

Correct answer:

Explanation:

When you have a number or value with a fractional exponent, 

or

So then,

Example Question #7 : Fractional Exponents

Find the value of 

Possible Answers:

Correct answer:

Explanation:

When you have a number or value with a fractional exponent, 

or

So then,

Example Question #8 : Fractional Exponents

Simplify:

Possible Answers:

Correct answer:

Explanation:

When exponents are raised to another exponent, you will need to multiply the exponents together.

When you have a number or value with a fractional exponent, 

or

So,

 

Example Question #9 : Fractional Exponents

Simplify:  

Possible Answers:

Correct answer:

Explanation:

An option to solve this is to split up the fraction.  Rewrite the fractional exponent as follows:

A value to its half power is the square root of that value.

Substitute this value back into .

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