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Maths Powers part 5 (Laws of Exponents) CBSE Class 8 Mathematics VIII
By ExamFear Education
Maths Powers part 5 (Laws of Exponents) CBSE Class 8 Mathematics VIII
More rational exponents and exponent laws | Algebra I | Khan Academy
By Khan Academy
Khan Academy presents More Rational Exponents and Exponent Laws, an educational video resource on math.
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.
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
ALL OF GRADE 9 MATH IN 60 MINUTES!!! (exam review part 1)
By Lumos Learning
Here is a great exam review video reviewing all of the main concepts you would have learned in the MPM1D grade 9 academic math course. The video is divided in to 3 parts. This is part 1: Algebra. The main topics in this section are exponent laws, polynomials, distributive property, and solving first degree equations. Please watch part 2 and 3 for a review of linear relations and geometry. If you watch all 3 parts, you will have reviewed all of grade 9 math in 60 minutes. Enjoy! Visit jensenmath.ca for more videos and course materials.
Exponent rules part 1 | Exponents, radicals, and scientific notation | Pre-Algebra | Khan Academy
By Khan Academy
Introduction to exponent rules
Negative exponents | Exponents, radicals, and scientific notation | Pre-Algebra | Khan Academy
By Khan Academy
How does a negative exponent affect our answer? Before you assume that the answer must be negative, think again!
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.
16 - Simplify Logarithms - Part 1 (Log Bases, Calculate Logarithms & More)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
Evaluating Logarithms | MathHelp.com
By MathHelp.com
In this example, notice that we have a polynomial divided by a binomial, and our binomial is in the form of an x term minus a constant term, or x – c. In this situation, instead of having to use long division, like we did in the previous lesson, we can divide the polynomials using synthetic division, which is a much more efficient method. Here’s how it works. We start by finding the value of c. Since –c = -3, we know that c = 3. Next, we put the value of c inside a box, so we put the 3 inside a box. It’s very important to understand that the number that goes inside the box always uses the opposite sign as the constant term in the binomial. In other words, since the constant term in the binomial is -3, the number that goes inside the box, is positive 3. Next, we write the coefficients of the dividend, which are 2, -7, 4, and 5. Be very careful with your signs. Now, we’re ready to start our synthetic division. First, we bring down the 2. Next, we multiply the 3 in the box times 2 to get 6, and we put the 6 under the -7. Next, we add -7 + 6 to get -1. Next, we multiply the 3 in the box times -1 to get -3, and we put the -3 under the 4. Next, we add 4 + -3 to get 1. Next, we multiply the 3 in the box times 1 to get 3, and we put the 3 under the 5. Finally, we add 5 + 3 to get 8. Now, notice that we have a 2, -1, 1, and 8 in the bottom row of our synthetic division. These values will give us our answer: the first 3 numbers represent the coefficients of the quotient, and the last number is the remainder. And it’s important to understand that our answer will be one degree less than the dividend. In other words, since our dividend starts with x cubed, and we’re dividing by x, our answer will start with x squared. So our answer is 2x squared – 1x + 1 + 8 over x – 3. Notice that we always use descending order of powers in our quotient. In this case x squared, x, and the constant. Finally, remember that we add the remainder over the divisor, just like we did in the previous lesson on long division, and we have our answer. It’s important to understand that we’ll get the same answer whether we use synthetic division or long division. However, synthetic division is much faster.
18 - Properties of Logarithms (Log x) - Part 1 - Laws of Logs - Calculate Logs & Simplify
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
Solving Logarithmic Equations | MathHelp.com
By MathHelp.com
Here we’re asked to evaluate each of the following logarithms. In part a, we have log base 7 of 49. To evaluate this logarithm, we set it equal to x. In other words, log base 7 of 49 = what? Notice that we now have an equation written in logarithmic form, so let’s see if we can solve the equation by converting it to exponential form. Remember that the base of the log represents the base of the power, the right side of the equation represents the exponent, and the number inside the log represents the result, so we have 7…to the x…= 49. Next, we solve for x. Notice that 7 and 49 have a like base of 7, so we rewrite 49 as 7 squared, and we have 7 to the x = 7 squared, so x must equal 2. In part b, we have log base 3 of 1/27. Again, to evaluate this logarithm, we set it equal to x, and convert the logarithmic equation to exponential form. Remember that the base of the log represents the base of the power, the right side of the equation represents the exponent, and the number inside the log represents the result, so we have 3…to the x…= 1/27. Next, we solve for x. Notice that 3 and 1/27 have a like base of 3, so we rewrite 1/27 as 1 over 3 cubed, and we have 3 to the x = 1 over 3 cubed. Next, 1 over 3 cubed is the same thing as 3 to the negative 3, so we have 3 to the x = 3 to the negative 3, which means that x must equal -3. Therefore, log base 3 of 1/27 = -3. So remember the following rule. To evaluate a logarithm, set it equal to x, convert to exponential form, and solve the equation using like bases.
08 - Solving Exponential Equations - Part 1 - Solve for the Exponent
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
06 - Proving the Logarithm (Log) Rules - Understand Logarithm Rules & Laws of Logs
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
15 - What is a Logarithm (Log x) Function? (Calculate Logs, Applications, Log Bases)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
04 - Solving Logarithmic Equations - Part 1 - Equations with Log(x)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
