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Zero, negative, and fractional exponents | Pre-Algebra | Khan Academy
By Khan Academy
Khan Academy presents Zero, Negative, and Fractional Exponents, an educational video resource on math.
Rational Exponents | MathHelp.com
By MathHelp.com
In this example, we’re asked to write “a” to the negative 3rd squared in simplest form without negative or zero exponents. Remember that the power rule tells us that when we have a power taken to another power, such as a to the negative 3rd squared, we multiply the exponents. So we have a to the -3 times 2, or a to the negative 6th. Finally, remember from our study of negative exponents that a to the negative 6th can be written as 1 over a to the positive 6th. So a to the negative 3rd squared simplifies to 1 over a to the 6th.
Negative Exponents | MathHelp.com
By MathHelp.com
In this example, we’re given the functions f(x) = 3x – 2 (read as “f of x equals…”) and g(x) = root x, and we’re asked to find the composite functions f(g(9)) (read as “f of g of 9”) and g(f(9). To find f(g(9)), we first find g(9). Since g(x) = root x, we can find g(9) by substituting a 9 in for the x in the function, to get g(9) = root 9, and the square root of 9 is 3, so g(9) = 3. Now, since g(9) = 3, f(g(9)) is the same thing as f(3), so our next step is to find f(3). And remember that f(x) = 3x – 2, so to find f(3), we substitute a 3 in for the x in the function, and we have f(3) = 3 times 3 minus 2. Notice that I always use parentheses when substituting a value into a function, in this case 3. Finally, 3 times 3 minus 2 simplifies to 9 minus 2, or 7, so f(3) = 7. Therefore, f(g(9)) = 7. Next, to find g(f(9), we first find f(9). Since f(x) = 3x - 2, we find f(9) by substituting a 9 in for the x in the function, to get f(9) = 3 times 9 minus 2, which simplifies to 27 – 2, or 25, so f(9) = 25. Now, since f(9) = 25, g(f(9)) is the same thing as g(25), so our next step is to find g(25). And remember that g(x) = root x, so to find g(25), we substitute a 25 in for the x in the function, to get g(25) = root 25. Finally, the square root of 25 is 5, so g(25) = 5. Therefore, g(f(9)) = 5. It’s important to recognize that
01 - Simplify Rational Exponents (Fractional Exponents, Powers & Radicals) - Part 1
By Math and Science
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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.
16 - Conjugate Root Theorem, Part 1 (Roots of Polynomials, Solving Polynomials & Conjugate Roots)
By Math and Science
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05 - Simplify Irrational Exponents, Part 1 (Radical Exponents, Powers, Pi & More)
By Math and Science
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18 - Descartes Rule of Signs, Part 1 (Find Roots of Polynomials)
By Math and Science
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11 - Learn ArcSin, ArcCos & ArcTan (Inverse Sin, Cos & Tan) - Part 1
By Math and Science
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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.
07 - What is an Exponential Function? (Exponential Growth, Decay & Graphing).
By Math and Science
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14 - Solve Quadratic Systems of Equations by Addition - Part 1 (Simultaneous Equations)
By Math and Science
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02 - Solve Perfect Square Quadratic Equations Part 1
By Math and Science
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04 - Solving Logarithmic Equations - Part 1 - Equations with Log(x)
By Math and Science
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