All Algebra II Resources
Example Question #1 : Distributing Exponents (Power Rule)
What is the largest positive integer, , such that is a factor of ?
. Thus, is equal to 16.
Example Question #2 : Distributing Exponents (Power Rule)
Simplify the expression:
Cannot be simplified
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 #3 : Distributing Exponents (Power Rule)
Order the following from least to greatest:
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 #4 : Distributing Exponents (Power Rule)
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 #5 : Distributing Exponents (Power Rule)
Use the power rule to distribute the exponent:
Example Question #6 : Distributing Exponents (Power Rule)
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 #7 : Distributing Exponents (Power Rule)
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 #8 : Distributing Exponents (Power Rule)
When faced with a problem that has an exponent raised to another exponent, the powers are multiplied: then simplify: .
Example Question #9 : Distributing Exponents (Power Rule)
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 #10 : Distributing Exponents (Power Rule)
Simplify this expression:
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.