Mathematical Relationships and Basic Graphs

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Algebra II › Mathematical Relationships and Basic Graphs

Questions 1 - 10
1

Evaluate

Explanation

When dealing with fractional exponents, we rewrite as such:

in which is the index of the radical and is the exponent raising base .

2

Which of the following is equivalent to ?

Explanation

The denominator of the powered term represents the root of the radical. The numerator of the fraction is the power that the quantity of the radical is raised by.

Note that the integer in front of the x-term will not be included inside the radical.

The answer is:

3

The answer is not present

Explanation

We can only combine radicals that are similar or that have the same radicand (number under the square root).

Combine like radicals:

We cannot add further.

Note that when adding radicals there is a 1 understood to be in front of the radical similar to how a whole number is understood to be "over 1".

4

Multiply the fractions:

Explanation

When multiplying fractions, multiply the numbers on the top together and the numbers on the bottom together. Then simplify accordingly.

5

Solve for .

Explanation

When we add exponents, we try to factor to see if we can simplify it. Let's factor . We get . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same.

With the same base, we can rewrite as .

6

Evaluate:

Explanation

To raise to the power of any positive integer, divide the integer by 4 and note the remainder. The correct power is given according to the table below.

Powers of i

, so can be determined by selecting the power of corresponding to remainder 1. The correct power is , so .

7

Simplify the following expression.

Explanation

Simplify the following expression

To simplify this, we need to subtract our exponents and divide our whole numbers.

When we do this, we get the following.

8

Explanation

When adding or subtracting radicals, the radicand value must be equal. Since and are not the same, we leave the answer as it is. Answer is .

9

Multiply:

Explanation

The bases of the exponents are common. This means we can add the fractions.

The least common denominator is six.

This becomes the power of the exponent.

Break up the fraction in terms so that each can be reduced.

Since we do not know term , it can be rewritten in base two, and .

Rewrite this term as a replacement of , and multiply the power of the exponent in base two with the power of the exponent in base eight.

Simplify the terms. A value to the power of one-half is the square root of that number.

The answer is:

10

Simplify .

Explanation

First multiply the like terms, remembering that when multiplying terms that have exponents, you add the exponents.

Negative exponents indicate that the term should be in the denominator, so the final answer is:

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