High School Math : Exponents

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #1 : Exponents

Which of the following is equivalent to  ? 

Possible Answers:

Correct answer:

Explanation:

By definition, 

.

In our problem,  and 

Then, we have .

Example Question #2 : Exponents

Solve for :

Possible Answers:

Correct answer:

Explanation:

Raise both sides of the equation to the inverse power of  to cancel the exponent on the left hand side of the equation.

Subtract  from both sides:

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 #1 : Understanding 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 #5 : Exponents

Which of the following is equivalent to  ?

Possible Answers:

Correct answer:

Explanation:

By definition, a number raised to the  power is the same as the square root of that number. 

Since the square root of 64 is 8, 8 is our solution. 

Example Question #1 : Simplifying Exponents

Simplify the following expression.

Possible Answers:

Correct answer:

Explanation:

When dividing with exponents, the exponent in the denominator is subtracted from the exponent in the numerator. For example: .

In our problem, each term can be treated in this manner. Remember that a negative exponent can be moved to the denominator.

Now, simplifly the numerals.

Example Question #2 : Simplifying Exponents

Simplify the following expression. 

 

Possible Answers:

Correct answer:

Explanation:

We are given: 

Recall that when we are multiplying exponents with the same base, we keep the base the same and add the exponents. 

Thus, we have .

Example Question #3 : Simplifying Exponents

Simplify the following expression. 

 

Possible Answers:

Correct answer:

Explanation:

Recall that when we are dividing exponents with the same base, we keep the base the same and subtract the exponents. 

Thus, we have .

We also recall that for negative exponents,

.

Thus, .

Example Question #4 : Simplifying Exponents

Simplify the following exponent expression:

Possible Answers:

Correct answer:

Explanation:

Begin by rearranging the terms in the numerator and denominator so that the exponents are positive:

Multiply the exponents:

Simplify:

Example Question #1 : Simplifying Exponents

Simplify the expression:

Possible Answers:

Correct answer:

Explanation:

First simplify the second term, and then combine the two:

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