In lesson 5 skill practice negative exponents on PDFfiller, you are going to find out some questions related to negative exponents. Apparently, this PDFfiller will be able to help you learn and practice negative exponents. To find out that information, just reading the following text.
Here are some questions for lesson 5 skill practice negative exponents on PDFfiller:
- Write each expression by using a positive exponent. (The questions for number 1-8).
- Evaluate each expression (The questions for number 9-12).
- Write each fraction as an expression by using a negative exponent. (The questions for number 13-16).
- Express by using positive exponents. (The questions for number 17-28).
The text above is a list of questions for lesson 5 skill practice negative exponents on PDFfiller. If you want to know those answers, you are able to see the image above. It is the answer key for lesson 5 skill practice negative exponents. However, if you want to know the answer key for lesson 5 skill practice negative exponents on PDFfiller here, simply you are able to see the text below. These are some answer keys for lesson 5.
There are lots of students already struggling to understand negative numbers and exponent rules. Understanding negative exponents is important for high school level math courses. It is also a concept students find challenging. Once you gradually build on your students’ knowledge, you will ensure that they are to solve challenging problems in the classroom. If you are not sure where to begin, this article is going to help you.
NEGATIVE EXPONENTS RULES
This is like everything else in math class, negative exponents also need to follow the rules. If you need a reminder, here is a list of the rules of exponents:
- Product of powers: This adds powers together once multiplying like bases.
- Quotient of powers rule: This subtract powers once dividing like bases.
- Power of powers rule: This multiply powers together once raising a power by another exponent.
- Power of a product rule: This distributes power to each base once raising some variables by a power.
- Power of a quotient rule: This distributes power to each base once raising some variables by a power.
- Zero power rule: This is any base raised to the power of zero becomes one.
- Negative exponent rule: This is to change a negative exponent to a positive one, just flip it into a reciprocal.
As a teacher, you have to remind students that the rules stay the same with negative exponents. There only might be a few extra steps to follow.
A QUICK REVIEW OF NEGATIVE NUMBERS
Negative numbers need a certain amount of abstract thinking that does not always come naturally. However, without a solid understanding of negative numbers, the students will not be ready to solve negative exponents. Here is a quick review:
Negative numbers are expressed with a negative sign. For example: , -4 is four less than zero. It is helpful to think of negative numbers as existing on a number line. Once you add and subtract negative numbers, you are either moving to the right or the left of the number line. Once you subtract a negative number you move to the left of the number line, because it is the same as adding a positive number. While if you are adding a negative number you move to the right because it is the same as subtracting a positive number. When you multiply a negative number by a positive number, the product is going to be negative. If you multiply 2 negative numbers or two positive numbers, the result is going to be positive.
WHAT DO NEGATIVE EXPONENTS MEAN?
We all already know that positive exponents are a method of expressing repeated multiplication. For example: 43=4x4x4=64. Apparently, there are a few different methods of thinking about negative exponents. However, generally negative exponents are the opposite of positive ones. All negative exponents are able to be expressed as their positive reciprocal. For your information, a reciprocal is a fraction where the numerator and denominator switch places.
MULTIPLYING AND DIVIDING NEGATIVE EXPONENTS
We have already covered multiplying exponents, but here is a quick review on how to multiply and divide negative exponents.
Multiplying negative exponents:
You have to note that the rules for multiplying exponents are the same, even once the exponent is negative. If the bases are the same, please add the exponents. Remember that the rules for adding and subtracting negative numbers. If the bases are different but the exponents are the same, so you are able to multiply the bases and leave the exponents the way they are. If there is nothing in common, you are able to go directly to solve the equation. Just flip the exponents into their reciprocals, then multiply it.
DIVIDING NEGATIVE EXPONENTS
Apparently, dividing negative exponents is almost the same as multiplying them, except you are doing the opposite: subtracting where you have added and dividing where you have multiplied. If the bases are the same, you are able to subtract the exponents. You have to remember to flip the exponent and create it positive, if needed. If the exponents are the same but the bases are different, you have to divide the bases first. If there is nothing in common, you have to go directly to solving the equation.
NEGATIVE NUMBERS WITH EXPONENTS
By the way, what happens if the base is negative instead of the exponents?
If the exponent is positive, you have to work with it as you will a regular exponent. However, you need to remember two things:
- If the base is negative and the exponent is a number, the final product is going to always be a positive number.
- If the base is negative and the exponent is an odd number, the final product is going to always be a negative number.
If there are parentheses around the negative base, so the power applies to the entire equation including the negative sign. But, if there are no parentheses, the power applies only to the base and not to the negative sign. Since the first example is being raised to an even power, the two negative signs cancel out and you are left with a positive product. If the exponent was an odd power, so the product will be negative as there will be one number that cannot cancel out.