Using Basic Rules of Exponents
Description/Explanation/Highlights
Video Description
This video will cover basic rules of using exponents in arithmetic operations.
Steps and Key Points to Remember
To simplify or solve problems with exponents, use the following steps:
- Follow Algebra order of operations when applying rules of exponents. i.e. Simplify whatever is in parenthesis first, then do operations to get rid of the parenthesis, then apply rules to multiply and divide and finally do addition or subtractiion.
- When values with like bases are multiplied together, add the exponents. i.e. \(x^4\cdot x^3=x^7\)
- When values with like bases are divided, subtract the exponents. i.e. \(\frac{x^7}{x^5} =x^2\)
- When values have a power that is raised to another power, multiply the exponents. i.e. \({(x^3)}^4=x^{12} \)
- Negative exponents are rewritten to positive and moved to the opposite part of the fraction. i.e. \(x^{-7}=\frac{1}{x^7} \)
- Anything raised to a power of 0 is equal to 1. i.e. \(249^0=1\) and also \( x^0=1\)
- When adding two values with exponents of the same base, add the coefficients NOT the exponents. i.e. \(x^6+x^6+x^6={3x}^6\)
Here are some key points to keep in mind when simplifying or solving with exponents:
- Do the parts that are in parenthesis first, then get rid of parenthesis.
- Apply the rules of exponents only to the exponents and their bases NOT to coefficients in front of them. Coefficients are just numbers and normal math rules apply to them. Be sure if you are raising a coefficient to a power, you do that and not just multiply. For example, \({(3x)}^2 \) is \(9x^2\) not \(6x^2 \) like many will mistakenly conclude.
- Be careful not to apply exponents to numbers outside of parenthesis. For example, \(3x^2 \) should only have the exponent applied to the x but not the 3 so it doesn’t change.
- All the same rules apply to negative exponents as to positive exponents. Be careful when dealing with fractions where a negative on top does not cancel a negative on the bottom.
Video Highlights
- 00:00 Introduction to rules of exponents
- 00:10 \( x^4 \cdot x^3\) example of adding exponents with like bases when multiplying
- 00:50 \(\frac{x^7}{x^5} \) example of subtracting exponents with like bases when dividing
- 01:03 \({(x^3)}^4\) example of multiplying exponents to raise a power to another power
- 01:30 \(x^{-4}\) example of rewriting negative exponents to make them positive
- 02:10 \(x^0\) example of raising anything to the zero power
- 02:40 \(x^6+x^6+x^6\) example of adding only coefficients of exponents with like bases when adding
- 03:50 \({2x}^4\cdot {5x}^3\) example of adding exponents with coefficients and like bases when multiplying
- 04:55 \(\frac{{21x}^8}{{7x}^3}\) example of dividing coefficients and subtracting exponents with like bases when dividing
- 05:30 \({({2x}^4)}^3\) example of raising a coefficient to a power and multiplying exponents to raise a power to another power
- 06:24 \(2{({3x}^4)}^2\) example of raising a coefficient to a power and multiplying exponents to raise a power to another power applied only to coefficients in the parenthesis
- 07:20 \(\frac{{(x^4\cdot x^2)}^3}{{(x^2)}^3}\) example of combining rules when dividing
- 08:25 \(\frac{x^{-5}\cdot x^2}{x^3}\) example of combining rules when dividing