\frac{z^{\frac{5}{4}} - z^{\frac{-1}{4}}}{z^{\frac{1}{3}}} Write your answer using only positive exponents. Simplify the following expression. The volume of a rectangle with length, breadth and height as 5x, 3x2 and 7x4 respectively is: Explanation: Volume of rectangle = Length × breadth × height. 1.\ \dfrac{x^2 - x}{x+5} \cdot \dfrac{x^2 + 5x + 4}{x^4 - x^2}\\ 2. a. - \dfrac{1}{7} - \dfrac{6}{7}, Perform the indicated operation and simplify. Write answer as integers or reduced fractions. Get help with your Algebraic expression homework. \frac{y^2-2y-15}{y^2-6y-27}, Simplify: \frac{(543 \times 64) + (\frac{432}{8} + 3)}{4 \times 2}. {3 n^{-5} z^7} / {n^{-8} z^9}, Simplify: \frac{(4 - x^2)}{(3x^2 - x - 10)} \cdot \frac{(6x)}{(8x + 16)}, Simplify the expression. Solve for x : \frac{1}{5}x + \frac{1}{4} = 3 \left(\frac{3}{4}x + 2 \right) . Write results in standard form. Simplify: \frac{x^2 - 5x + 6}{x^2 - x - 2} \cdot \frac{x^3 + 27}{x^2 - 9}. \left ( -\frac{2}{3} \right )^2, Evaluate the expression. Simplify the expression: \frac{\sqrt[3]{8m^2n^3} \cdot \sqrt[3]{2m^2}}{\sqrt[3]{32m^4n^3}} . Practice questions In the following questions, solve for x in each case just by looking at the equation. If you haven't studied this lesson yet, click here. (4x - 7) + (3x^2 - 5x + 9). GCSE Revision Cards. Add and simplify: 4 / {m + 2} + 2 / {m - 2} Choose one answer. A term is the product of factors. Assume that all variables represent positive real numbers. 8. 10. If we multiply 5x and (– 4xyz), then we get: Explanation: Anything multiplied by zero is zero. If the website received 13,455 visits over the three-... Simplify the following expression and select the correct one. {3 x^3 + 2 x^2 - x} / {x + 7} / {3 x^2 - x} / {x^2 + 14 x + 49}. c. {4 b} / {5 a}. Now that you've studied the three detailed examples for Simplfying Algebraic Expressions, you are ready to try some on your own! (b) Work out the value of r, if the perimeter is 49 cm. A financial advisor has invested $5,000 in two accounts. Simplify the expression: 9(6yx + 10) - (6yx - 5). 4. Copyright Â© 2009-2020 | Karin Hutchinson | ALL RIGHTS RESERVED. An algebraic expression is a combination of letters called _____ and real numbers called _____. algebraic. Solve and simplify: \frac{\frac{4x^2a}{y^2}+\frac{1}{a^2}}{2-\frac{2}{y^2a^2}}. 6 xy + 11. b. In general, an expression with one or more than one term (with nonnegative integral exponents of the variables) is called a ‘Polynomial’. We use cookies to ensure that we give you the best experience on our website. Question 8 : Write the algebraic expressions for the following : x more than two-third of y. State any restrictions on the variable. State the name of the property illustrated: (6 + 3) + (1 + 16) = (1 + 16) + (6 + 3). \frac{x^2 - 43}{x^2 - 4x - 5} = \frac{5}{x + 1} - \frac{3}{ x - 5}. 12s^{2} - 5st + 24t^{2} + 10s^{2} - 2t^{2} + 60st + 10t^{2}, Divide the Fraction: \frac{\frac{3xy + x}{y^2 - y}}{\frac{3y + 1}{xy}}, Divide: \frac{(X^3 - 2X^2 + 4X - 5)}{(X + 3)} = \boxed{\space}. Express in the standard form: (5.2 x 10^(17))/(-1.3 x 10^(-5)). (-15x^{3} + 8x^{2} + 22x + 5) \div (-3x + 4) A) 5x^{2} + 4x - 2 B) 5x^{2} + 4x - 2 + \frac{13}{-3x + 4} C) x^{2} - 2 + \frac{4}{-3x + 4} D) 5x^{2} + 4x - 2 + \frac{16}{-3x + 4}. Be very careful as you simplify your terms and make sure that you On this site, I recommend only one product that I use and love and that is Mathway If you make a purchase on this site, I may receive a small commission at no cost to you. Simplify the expression y^2 + 9y + 20 / y^2 + 12y + 32. 9x^2 - 4 - 10 x^2 + 10 + 3x, Use the rules of exponents to simplify the expression. Find the exponent if the expression 5(x^4)^2 is to be written in kx^p form. They won 24 more than they lost. All material on this website is for reference purposes only and does not represent the actual format, pattern from respective official authority. a. (\frac{4x^5y^{-2}}{3x^{-4}})^4, Solve for the variable in the following equation. Simplify and state the restrictions. Earn Transferable Credit & Get your Degree, Simplify. Services, Working Scholars® Bringing Tuition-Free College to the Community. Simplify the complex rational expression. Write the following as an algebraic expression the simplify. How many games did they win? (x + 5 )(x^2 - x + 7), Simplify this expression. Perform the following additions and/or subtractions: (4x^2 + x + 10) + (10x^2 + 9x + 11 ). ____________________, Ab(c) = (ab)c is an example of what property? Now that you've studied the three detailed examples for Simplfying Algebraic Expressions, you are ready to try some on your own! 13y c. -13y d. x + 13y, Solve using the addition and multiplication principles together and also check the result. (8.3x - 2.9) - (9.6x - 4.8), Simplify the expression. Multiple choice questions (MCQs) are available for Class 8 Algebraic Expressions and Identities chapter. Then simplify. \frac{8}{5x^{-2/3}}, Add. \frac{9 - \sqrt{25}}{-2|1 - 2|^{2}}, Simplify the expression. {18 x^6} / {y^5}. 5x^3y^3\sqrt{3x} \\c. c. {6m + 12} / {(m + 2) (m -2)}. Two times the product of a and b divided by 5 : Sum of numbers m and n decreased by their product : Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here. 7(y - 3) - 4(y + 2) = 3(y - 7), Add \left ( \frac{1}{4}x^4 +\frac{6}{7}x^3+\frac{7}{8}x^2+3 \right )+\left ( -\frac{3}{4}x^4+\frac{1}{8}x^2-3 \right ) = _____. Test your understanding with practice problems and step-by-step solutions. x = \frac{-13}{3} \\c. When dealing with simple algebraic expressions, you don’t always need algebra to solve them. \frac{40}{x^2 - 16} - \frac{5}{x - 4} = \frac{2}{x + 4}. But when Melissa applied the distributive law and multiplied out 2x(14x - 3x - 5x), she got 28x - 6x - 10x ; thus, Andrew's solut... Simplify the expression \frac{5ab}{10ab}. Express your answer as an integer. \frac{3x^{3} - 4x^{2}y + xy^{2}}{9x^{2}y - y^{3}}, Simplify the expression. {b^n 5^{n + 1}} / {5^n b^{n + 1}}. \frac{5}{6}(\frac{3}{5}x + 12y) - \frac{1}{4}(2x - 12y) a. The actual exam may differ from our materials. Quiz: Which Anime Character Are You Most Like. \bigg(\frac{4p^{-3}q}{3^{-1}m^3}\bigg) ^2, Simplify: \displaystyle \frac{\frac{\frac{2}{b + 2}}{1}}{\frac{b - 2 + 1}{b^2 - 4}}, Write the expression with rational exponents 6\sqrt{(-8x)^5}, Write the rational expression in lowest terms. {x^2} / {2 y}. Assume all variables represent nonzero real numbers. \frac{b^3 + b^2}{b + 1} \\2. Solve. Here, 3x, 2y and 6 are three terms. Write with positive exponents. These multiple-choice questions have been designed by experts referring to the latest CBSE syllabus and NCERT guidelines. If false, correct the expression to make it true. A website received 9,347 visits during the first month of its launch. \displaystyle\frac{\frac{r+2s}{20}}{\frac{8r+16s}{5}}, Complete the following operations: a) \frac{y^6}{y^{-7}}\\, Simplify. All rights reserved. (9x - 12) - (6x + 1), Simplify the following expression: 12x^2-6+5x-8x^2-9, Simplify the given expression. Translate this sentence into an equation. Algebraic Expressions Practice Test Questions Answers: An algebraic expression is formed from variables and constants using different operations.