Algebra II : Exponents

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #231 : Understanding Exponents

Convert  to base .

Possible Answers:

Correct answer:

Explanation:

First, we know that  is divisible by .

Therefore:

The answer is:

Example Question #232 : Understanding Exponents

Convert  to base .

 

Possible Answers:

Correct answer:

Explanation:

First, we know  is divisible by .

Therefore:

 

We can set-up an equation by applying the power rule of exponents.

 

When a number to a power is raised by an exponent, we add the exponents. Write an equation and solve for .

Simplify.

The answer is:

Example Question #233 : Understanding Exponents

Convert  to base .

Possible Answers:

Correct answer:

Explanation:

First, know  is divisible by .

Therefore:

 

We can set-up an equation by applying the power rule of exponents.

 

When a number to a power is raised by an exponent, we add the exponents. Write an equation and solve for .

Simplify.

The answer is:

Example Question #231 : Exponents

Convert  to base 

Possible Answers:

Correct answer:

Explanation:

First, we know the following:

 

In order to figure out the whole exponent, we can apply the power rule for exponents.

Example Question #232 : Exponents

Evaluate:

Possible Answers:

Correct answer:

Explanation:

We can expand  to the following:

  

The product is: 

Example Question #236 : Understanding Exponents

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

We can expand  to the following:

The product is: 

Example Question #237 : Understanding Exponents

Convert  to base 

Possible Answers:

Correct answer:

Explanation:

First, we know that  is divisible by .

The conversion becomes: 

 

Example Question #238 : Understanding Exponents

Convert  to base .

Possible Answers:

Correct answer:

Explanation:

First, we know that  is divisible by .

The conversion becomes: 

 

Example Question #3371 : Algebra Ii

Convert  to base 

Possible Answers:

Correct answer:

Explanation:

We know that exponents raised to the negative power will generate fractions. 

We also know that  is divisible by .

 

However, since this a fraction, we then have the following:

Example Question #3372 : Algebra Ii

Convert  to base 

Possible Answers:

Correct answer:

Explanation:

If fractions are raised to a positive integer exponents, we know we will generate fractions; however, if a fraction is raised by a negative integer exponent, our answer will be whole number instead.

For example: 

The following rule has been used in this scenario:

 

In this formula,  is a positive exponent raising the base .

We know .

Since we are dealing with a integer and converting to fractional base, we know we need to have a negative exponent.

The answer is:

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