Laws of Exponents

polynomials and Laws of Exponents

By Chi Riemann

objectives

1. Define a general polynomial.

2. Classify polynomials​ according to number of terms.

3. Use laws of exponents to simplify expressions.​

Math 1 | Polynomials

Definitions, Laws of Exponents

Multiple Choice

Which of the following is not a polynomial?

• $$\frac{x^2}{4}$$  

• $$\frac{5}{x}$$  

• $$-3x^5$$  

• $$-x^2+\frac{x}{3}$$  

definition

Polynomials and Laws of Exponents

Multiple Select

Identify all the polynomials.

• $$\frac{1}{2x}$$  

• $$y^{0.5}$$  

• $$7^{-2}$$  

• $$\frac{2x}{y+1}$$  

• $$4x^2-2x+1$$  

definitions

Multiple Choice

What is the degree of $$-7xy^3$$ ?

• $$1$$  

• $$3$$  

• $$4$$  

Degree of a monomial

Polynomials and Laws of Exponents

Multiple Choice

Simplify $$x^5\cdot x^8$$ .

• $$x^{13}$$  

• $$x^{40}$$  

• $$2x^{13}$$  

product rule

Polynomials and Laws of Exponents

Multiple Choice

Simplify $$\left(x^2\right)^3$$ .

• $$x^5$$  

• $$x^6$$  

• $$x^8$$  

power of a power rule

Polynomials and Laws of Exponents

Multiple Choice

Simplify $$\left(xy\right)^5$$ .

• $$x^5y^5$$  

• $$xy^5$$  

• $$x^5y$$  

power of a product rule

Polynomials and Laws of Exponents

Multiple Choice

Simplify $$\frac{x^7}{x^3}$$ .

• $$\frac{1}{x^4}$$  

• $$x^4$$  

• $$4$$  

quotient rule

Polynomials and Laws of Exponents

Multiple Choice

Simplify $$\left(\frac{x}{y}\right)^3$$ .

• $$\frac{x}{y^3}$$  

• $$\frac{x^3}{y}$$  

• $$\frac{x^3}{y^3}$$  

power of a quotient rule

Polynomials and Laws of Exponents

Multiple Choice

Assuming that $$x\ne0$$  , simplify $$\left(4x\right)^0$$ .

• $$4$$  

• $$1$$  

• $$0$$  

zero exponent rule

Polynomials and Laws of Exponents

Multiple Choice

Simplify $$x^{-5}$$ .

• $$\frac{1}{x^5}$$  

• $$\frac{x}{x^5}$$  

• $$\frac{x}{5}$$  

negative exponent rule

Polynomials and Laws of Exponents

Multiple Choice

Simplify $$3x^4\cdot4x^5$$ .

• $$12x^9$$  

• $$7x^9$$  

• $$12x^{20}$$  

• $$7x^{20}$$  

Multiple Choice

Simplify $$-5x\left(12xy\right)$$ .

• $$-60xy$$  

• $$7x^2y$$  

• $$-60x^2y$$  

Multiple Choice

Simplify $$-3^{-2}$$ .

• $$\frac{1}{9}$$  

• $$-\frac{1}{9}$$  

• $$\frac{1}{6}$$  

• $$-\frac{1}{6}$$  

Multiple Choice

Simplify $$\left(-\frac{1}{4}\right)^{-2}$$ .

• $$16$$  

• $$-16$$  

• $$\frac{1}{16}$$  

• $$-\frac{1}{16}$$  

Multiple Choice

Simplify $$\frac{2^{-2}}{3^{-2}}$$ .

• $$-\frac{4}{9}$$  

• $$-\frac{9}{4}$$  

• $$\frac{4}{9}$$  

• $$\frac{9}{4}$$  

Multiple Choice

Simplify $$2x\cdot x^2$$ .

• $$2x^2$$  

• $$2x^3$$  

• $$4x^2$$  

• $$4x^3$$  

Multiple Choice

Simplify $$xy^2\cdot x^2y$$ .

• $$x^3y^3$$  

• $$x^2y^2$$  

• $$x^6y$$  

• $$xy^6$$  

Multiple Choice

Simplify $$2x^3\cdot2x^2$$  

• $$2x^6$$  

• $$4x^6$$  

• $$4x^5$$  

• $$2x^5$$  

Multiple Choice

Assuming that $$x\ne-\frac{1}{4}$$  , simplify $$-\left(4x+1\right)^0$$  .

• $$0$$  

• $$1$$  

• $$-1$$  

• $$-4$$  

Multiple Choice

Simplify $$\left(2mn^3\right)^2\left(mn\right)^3$$ .

• $$4m^6n^8$$  

• $$4m^5n^{12}$$  

• $$4m^5n^9$$  

• $$2m^5n^8$$  

Multiple Choice

Assuming that $$x,y\ne0$$  , simplify $$\left(\frac{x^2}{2x^0y^3\cdot3y^2}\right)^2$$ .

• $$\frac{x^4}{36y^{10}}$$  

• $$\frac{x^4}{40y^{10}}$$  

• $$\frac{x^4}{36y^{13}}$$  

• $$\frac{x^4}{40y^{13}}$$  

Multiple Choice

Assuming that $$x,y\ne0$$ , simplify $$2x^{-1}y^{-2}\cdot\left(2x^{-1}y^{-2}\right)^3$$ .

• $$\frac{1}{16x^4y^8}$$  

• $$\frac{16}{x^4y^8}$$  

• $$\frac{12}{x^4y^8}$$  

• $$\frac{16}{x^4y^{10}}$$  

Multiple Choice

Assuming that $$x,y\ne0$$ , simplify $$2x^{-3}y^{-2}\cdot\left(2x^0y^3\right)^3$$ .

• $$\frac{6y^7}{x^3}$$  

• $$\frac{8y^7}{x^3}$$  

• $$\frac{12y^7}{x^3}$$  

• $$\frac{16y^7}{x^3}$$  

references

Redden, J. (2012). Beginning Algebra. http://2012books.lardbucket.org/

​

Wallace, T. (2010). Beginning and Intermediate Algebra. http://wallace.ccfaculty.org/book/book.html​

Polynomials and Laws of Exponents