Algebra II : Distributing Exponents (Power Rule)

Example Questions

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Example Question #1 : Distributing Exponents (Power Rule)

What is the largest positive integer, , such that is a factor of ?

10

20

16

8

5

16

Explanation: . Thus, is equal to 16.

Example Question #1 : Expressions & Equations

Simplify the expression: Cannot be simplified     Explanation:

Begin by distributing the exponent through the parentheses. The power rule dictates that an exponent raised to another exponent means that the two exponents are multiplied: Any negative exponents can be converted to positive exponents in the denominator of a fraction: The like terms can be simplified by subtracting the power of the denominator from the power of the numerator:  Example Question #1 : Distributing Exponents (Power Rule)

Order the following from least to greatest:           Explanation:

In order to solve this problem, each of the answer choices needs to be simplified.

Instead of simplifying completely, make all terms into a form such that they have 100 as the exponent.  Then they can be easily compared.  , , and .

Thus, ordering from least to greatest: .

Example Question #1 : Distributing Exponents (Power Rule)

Simplify:       Explanation: Step 1: Distribute the exponents in the numberator. Step 2: Represent the negative exponents in the demoninator. Step 3: Simplify by combining terms.  Example Question #1 : Distributing Exponents (Power Rule)

Simplify:       Explanation:

Use the power rule to distribute the exponent: Example Question #1 : Distributing Exponents (Power Rule)

Simplify:       Explanation:

Step 1: Distribute the exponent through the terms in parentheses: Step 2: Use the division of exponents rule.  Subtract the exponents in the numerator from the exponents in the denominator: Example Question #3 : Distributing Exponents (Power Rule)

Simplify.       Explanation:

When a power applies to an exponent, it acts as a multiplier, so 2a becomes 4a and -b becomes -2b. The negative exponent is moved to the denominator.

Example Question #4 : Distributing Exponents (Power Rule)

Simplify .      Explanation:

When faced with a problem that has an exponent raised to another exponent, the powers are multiplied: then simplify: .

Example Question #5 : Distributing Exponents (Power Rule)

Solve:       Explanation:

Solve each term separately.  A number to the zeroth power is equal to 1, but be careful to apply the signs after the terms have been simplified. Example Question #6 : Distributing Exponents (Power Rule)

Simplify this expression:       Explanation: is the correct answer because the order of operations were followed and the multiplication and power rules of exponents were obeyed. These rules are as follows: PEMDAS (parentheses,exponents, multiplication, division, addition, subtraction), for multiplication of exponents follow the format , and . First we simplify terms within the parenthesis because of the order of operations and the multiplication rule of exponents: Next we use the power rule to distribute the outer power: = **note that in the first step it isn't necessary to combine the two x powers because the individuals terms will still add to x^16 at the end if you use the power rule correctly. However, following the order of operations is a great way to avoid simple math errors and is relevant in many problems.

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