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Simplifying a radical expression using rational exponents
By Brain McLogan
Learn how to simplify rational powers using the power and the product rules. There are some laws of exponents which might come handy when simplifying expressions with exponents. Some of the laws include the product law which states that the product of numbers/expressions having the same base is equivalent to taking one of the base with the sum of the original exponents as the new exponent. The power law says that when an expression with an exponent is raised to another exponent that it is equivalent to the expression with the product of the original exponents as the new exponent. Knowledge of these exponent laws will help you in simplifying power expressions using the power rule and the quotient rule.
Solving Natural Logarithms | MathHelp.com
By MathHelp.com
In this example, we’re asked to expand the given logarithmic expression, log base 3 of M squared N to the 5th. Remember that our first law of logarithms states that if two values are multiplied together inside a logarithm, such as M squared times N to the 5th, then we can expand the logarithm into the sum of two separate logarithms, in this case log base 3 of M squared plus log base 3 of N to the 5th. Next, notice that each logarithm has a power inside the logarithm, and remember that our third law of logarithms states that if we have a power inside a logarithm, we can move the exponent to the front of the logarithm, so we have 2 times log base 3 of M + 5 times log base 3 of N.
Logarithm Rules: Expanding Logarithms | MathHelp.com
By MathHelp.com
To simplify 81 to the ½, remember from our study of rational exponents that an exponent of ½ means that we take the square root of the base. In other words, 81 to the ½ means the same thing as the square root of 81. And the square root of 81 is 9. So 81 to the ½ is 9
21 - Pascals Triangle & Binomial Expansion - Part 1
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
16 - The Geometric Series - Definition, Meaning & Examples - Part 1
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
Arithmetic Sequences and Arithmetic Series - Basic Introduction
By The Organic Chemistry Tutor
This video provides a basic introduction into arithmetic sequences and series. It explains how to find the nth term of a sequence as well as how to find the sum of an arithmetic sequence. It also discusses how to distinguish a finite sequence from an infinite series. It also includes a few word problems.
Grade 5 Math - Divide Decimals
By Lumos Learning
Using the Lumos Study Programs, parents and educators can reinforce the classroom learning experience for children and help them succeed at school and on the standardized tests. Lumos books, dvd, eLearning and tutoring are used by leading schools, libraries and thousands of parents to supplement classroom learning and improve student achievement in the standardized tests.
Logarithms - What is e? | Euler's Number Explained | Don't Memorise
By Don't Memorise
What is e? What is Euler's Number or Euler's Identity? What is the Natural Logarithm or logs? what is a logarithmic function? Watch this logarithms tutorial to know the answers to all these questions also learn how the value of Euler's Number is calculated.
Geometric Series and Geometric Sequences - Basic Introduction
By The Organic Chemistry Tutor
This video provides a basic introduction into arithmetic sequences and series. It explains how to find the nth term of a sequence as well as how to find the sum of an arithmetic sequence. It also discusses how to distinguish a finite sequence from an infinite series. It also includes a few word problems.
10 - Series and Sigma Summation Notation - Part 1 (Geometric Series & Infinite Series)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
01 - Visualize Roots of Equations - Linear, Quadratic, Cubic, Quartic Solutions
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
Integration By Partial Fractions
By The Organic Chemistry Tutor
This calculus video tutorial provides a basic introduction into integrating rational functions using the partial fraction decomposition method. Partial fraction decomposition is the process of breaking a single complex fraction into multiple simpler fractions. The integrals of many rational functions lead to a natural log function with absolute value expressions. This video explains what to do when you have repeated linear factors and quadratic factors. This tutorial contains many examples and practice problems on integration by partial fractions.
