# Use rational exponents to write a single radical expression

Simplifying radical expressions Video transcript What I want to do in this video is resimplify this expression, 3 times the principal root of times x to the third, and take into consideration some of the comments that we got out on YouTube that actually give some interesting perspective on how you could simplify this. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Grade 4 Arkansas 4. Use this principle to recognize and generate equivalent fractions.

Recognize that comparisons are valid only when the two fractions refer to the same whole.

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Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation.

Add and subtract mixed numbers with like denominators, e. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e. Solve word problems involving multiplication of a fraction by a whole number, e.

Between what two whole numbers does your answer lie? For example, rewrite 0. Recognize that comparisons are valid only when the two decimals refer to the same whole. Represent verbal statements of multiplicative comparisons as multiplication equations.

Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 — is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 - is prime or composite.

Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule 'Add 3' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers.

Explain informally why the numbers will continue to alternate in this way. Grade 4 Arkansas 5. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond e.

Grade 5 Arkansas 5.Multiplication Worksheets Dynamically Created Multiplication Worksheets. Here is a graphic preview for all of the multiplication worksheets. You can select different variables to customize these multiplication worksheets for your needs.

Derivatives of Power Functions and Polynomials. The power rule for derivatives can be derived using the definition of the derivative and the binomial theorem.

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The result is the following theorem: If f(x) = x n then f '(x) = nx n Polynomials are sums of power functions. A worked example of simplifying radical with a variable in it. In this example, we simplify 3√(x³). An nth root of a number x, where n is a positive integer, is any of the n real or complex numbers r whose nth power is x:.

Every positive real number x has a single positive nth root, called the principal nth root, which is alphabetnyc.com n equal to 2 this is called the principal square root and the n is omitted. The nth root can also be represented using exponentiation as x 1/n.

ALGEBRA in WORDS: A Guide of Hints, Strategies and Simple Explanations - Kindle edition by Gregory Bullock. Download it once and read it on your Kindle device, PC, phones or tablets.

Use features like bookmarks, note taking and highlighting while reading ALGEBRA in WORDS: A Guide of Hints, Strategies and Simple Explanations. The \(x\) in the log equation is called the argument and it must be greater than 0, again, to avoid complex numbers.

Simplifying square roots (variables) | Algebra (video) | Khan Academy