91Ó°ÊÓ

In Exercises \(85-94,\) simplify using properties of exponents. $$\left(3 x^{2 / 3}\right)\left(4 x^{3 / 4}\right)$$

What is an algebraic expression? Give an example with your explanation.

The polynomial \(-0.02 A^{2}+2 A+22\) is used by coaches to get athletes fired up so that they can perform well. The polynomial represents the performance level related to various levels of enthusiasm, from \(A=1\) (almost no enthusiasm) to \(A=100\) (maximum level of enthusiasm). Evaluate the polynomial for \(A=20, A=50,\) and \(A=80 .\) Describe what happens to performance as we get more and more fired up.

In Exercises 85-94, factor and simplify each algebraic expression. $$x^{3 / 4}-x^{1 / 4}$$

Perform the indicated operation and express the answer in decimal notation. $$ \frac{6.3 \times 10^{3}}{3 \times 10^{5}} $$

In Exercises 85-94, factor and simplify each algebraic expression. $$4 x^{-2 / 3}+8 x^{1 / 3}$$

Why is \(3(x+7)-4 x\) not simplified? What must be done to simplify the expression?

In Exercises \(85-94,\) simplify using properties of exponents. $$\frac{20 x^{1 / 2}}{5 x^{1 / 4}}$$

The number of people who catch a cold t weeks after January 1 is \(5 t-3 t^{2}+t^{3} .\) The number of people who recover \(t\) weeks after January 1 is \(t-t^{2}+\frac{1}{3} t^{3}\). Write a polynomial in standard form for the number of people who are still ill with a cold \(t\) weeks after January 1

In Exercises \(85-94,\) simplify using properties of exponents. $$\frac{72 x^{3 / 4}}{9 x^{1 / 3}}$$