# Solutions for Lesson 2 Practice Questions

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Contents

## Notation

Simplify the following.

a) x \cdot x \cdot x \cdot x \cdot x = ?

x^5

b) x+x+x+x+x=?

5x

c) 2x+x+x+x=?

5x

d) 2x\cdot x \cdot x \cdot x = ?

2x^4

e) x^2+x+x+x=?

x^2+3x

f) x^2\cdot x \cdot x \cdot x=?

x^5

## Vocabulary

a) How many terms are there in the expression x^3+(3x)(2y)-7x+\frac{2}{x}?

4

b) Which term prevents x^3+(3x)(2y)-7x+\frac{2}{x} from being a polynomial?

\frac{2}{x}

c) What is the degree of the polynomial xy^3+4x^3y^8-3xy^2?

11

## Exponents

What is the base and exponent for each term? What does each term equal?

a) 5^4=?

625

base:

5

exponent:

4

b) 5^{-4}=?

\frac{1}{625}

base:

5

exponent:

-4

c) -5^{-4}=?

-\frac{1}{625}

base:

5

exponent:

-4

d) (-5)^{-4}=?

-\frac{1}{625}

base:

-5

exponent:

-4

## Simplification

Simplify each of the following expressions:
a) 3x-5y+6x

3x-5y+6x=3x+6x-5y=9x-5y

b) 3x^2+2x+4x^2

3x^2+2x+4x^2=3x^2+4x^2+2x=7x^2+2x

c) (3x^2)(-5y^3)(6x)

(3x^2)(-5y^3)(6x) = (3)(x^2)(-5)(y^3)(6)(x) = (3)(-5)(6)(x^2)(x)(y^3) = -90x^3y^3

d) (3x^2)(-5y^3)(-6z)

(3x^2)(-5y^3)(-6z) = (3)(x^2)(-5)(y^3)(-6)(z)= (3)(-5)(-6)(x^2)(y^3)(z) = 90x^2y^3z

e) 2x(3y)z+(-5y)(2z)(-10x)-xzy

2x(3y)z+(-5y)(2z)(-10x)-xzy = (2)(x)(3)(y)(z)+(-5)(y)(2)(z)(-10)(x)-xzy = 6xyz+100xyz-xyz = 105xyz

f) \frac{3x^2y^3z}{6xyz^7}

\frac{3x^2y^3z}{6xyz^7} = \frac{3}{6}(x^2)(x^{-1})(y^3)(y^{-1})(z)(z^{-7}) = \frac{1}{2}(x^{2-1})(y^{3-1})(z^{1-7}) = \frac{1}{2}xy^2z^{-6} = \frac{xy^2}{2z^6}