91Ó°ÊÓ

Factor and simplify each algebraic expression. $$(4 x-1)^{\frac{1}{2}}-\frac{1}{3}(4 x-1)^{\frac{3}{2}}$$

In Exercises 103–106, determine whether each statement makes sense or does not make sense, and explain your reasoning. Knowing the difference between factors and terms is important: In \(\left(3 x^{2} y\right)^{2},\) I can distribute the exponent 2 on each factor, but in \(\left(3 x^{2}+y\right)^{2},\) I cannot do the same thing on each term.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Many English words have prefixes with meanings similar to those used to describe polynomials, such as monologue, binocular , and tricuspid.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. In one short sentence, five words or less, explain what $$\frac{\frac{1}{x}+\frac{1}{x^{2}}+\frac{1}{x^{3}}}{\frac{1}{x^{4}}+\frac{1}{x^{5}}+\frac{1}{x^{6}}}$$ does to each number \(x\).

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. A number decreased by the sum of the number and four.

What difference is there in simplifying \(\sqrt[3]{(-5)^{3}}\) and \(\sqrt[4]{(-5)^{4} ?}\)

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. Ten times the product of negative four and a number.

What is a perfect square trinomial and how is it factored?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.

$$\text { factor completely.}$$ $$-x^{2}-4 x+5$$