Unit 9 Remediation

Multiple Choice

What is the exponential form of 3𑁦3𑁦3𑁦3𑁦3𑁦3𑁦3𑁦3

• 3⁸

• 24

• 8³

• x⁸

Multiple Choice

$$\left(6x^2\right)\left(3x^{-5}\right)$$  

• $$\frac{18}{x^{10}}$$  

• $$18x^3$$  

• $$\frac{18}{x^3}$$  

• $$\frac{1}{18x^3}$$  

Multiple Choice

What is the expanded form of x^5?

• x𑁦x𑁦x𑁦x𑁦x

• 5𑁦x

• x+x+x+x+x

• 5x

Rule #1: Power of zero

Multiple Choice

5⁰

• 1

• 5

• 0

Multiple Choice

5x⁰

• 1

• 5

• 5x

• 0

Multiple Choice

(5xy)⁰

• 1

• 5

• 5xy

• 0

Rule #2: Negative exponents

Multiple Choice

x^-3

• -3x

• 1/x³

• x³

Multiple Choice

4^-2

• 16

• -16

• 1/16

• -1/16

Rule # 3: Multiplying with exponents

Multiple Choice

Product Rule

When multiplying exponents with the same base, _______ the exponents.

• subtract

• add

• multiply

• divide

Multiple Choice

$$x^3\cdot x^4\ =$$  

• $$x^{12\ }$$  

• $$x^{-1}$$  

• $$x^7$$  

• $$x^{34}$$  

Multiple Choice

Simplify:

$$\left(-2a^2b\right)\cdot\left(7a^3b\right)$$  

• $$5a^3b^2$$  

• $$-14a^5b^2$$  

• $$-14a^5b$$  

• $$-14a^6b^2$$  

Rule #4: Dividing with exponents

Multiple Choice

The quotient rule says that when you are dividing two exponents with the same base, you keep the base and __________ the exponents.

• Add

• Subract

• Multiply

• Divide

Multiple Choice

$$\frac{x^9}{x^4}$$  =

• $$x^{13}$$  

• $$x^{36}$$  

• $$x^5$$  

• $$x^{-5}$$  

Multiple Choice

Simplify:

$$\frac{27x^6}{9x}$$  

• $$3x^7$$  

• $$3x^5$$  

• $$3x^6$$  

• $$3x^4$$  

Rule #5: Raising a power to a power

Multiple Choice

Simplify:

$$\left(x^4\right)^5$$  

• $$x^{20}$$  

• $$x^9$$  

• $$x^{12}$$  

• $$x^{-1}$$  

Multiple Choice

Simplify:

$$\left(-2m^5\right)^2$$  

• $$-4m^7$$  

• $$-4m^{10}$$  

• $$4m^7$$  

• $$4m^{10}$$  

Multiple Choice

Simplify:

$$\frac{\left(y^2\right)^3}{y^4}$$  

• $$y^2$$  

• $$y$$  

• $$y^{12}$$  

• $$y^{10}$$  

Multiple Choice

$$\left(5x^2y^4\right)^3$$  

• $$125x^6y^{12}$$  

• $$15x^6y^{12}$$  

• $$8x^5y^7$$  

• $$15x^5y^7$$  

Multiple Choice

$$b^3\cdot b^4\cdot b^7\cdot b$$  

• $$b^{15}$$  

• $$b^{14}$$  

• $$b^{84}$$  

• $$b^{49}$$  

Multiple Choice

$$\frac{9a^3b^5}{-3ab^2}$$  

• $$-3a^2b^3$$  

• $$6a^2b^3$$  

• $$3a^3b^3$$  

• $$-\frac{1}{3}a^2b^3$$  

Multiple Choice

$$7^0$$  

• 1

• 7

• 0

• 70

Multiple Choice

$$\frac{xy^7}{x^3y^4}$$  

• $$\frac{y^3}{x^2}$$  

• $$x^2y^3$$  

• $$\frac{x^2}{y^3}$$  

• $$\frac{y^3}{x^3}$$  

Multiple Choice

$$\left(7xy\right)^2$$  

• $$49x^2y^2$$  

• $$14x^2y^2$$  

• $$49x^3y^3$$  

• $$14x^3y^3$$  

Multiple Choice

$$\left(6x^2\right)\left(3x^{-5}\right)$$  

• $$\frac{18}{x^{10}}$$  

• $$18x^3$$  

• $$\frac{18}{x^3}$$  

• $$\frac{1}{18x^3}$$  

Multiple Choice

$$8x^0$$  

• 8

• 1

• 0

• x

Multiple Choice

$$\left(\frac{3m^2n^7}{m}\right)^5$$  

• $$243m^5n^{35}$$  

• $$15m^{10}n^{35}$$  

• $$\frac{243n^{35}}{m^5}$$  

• $$15m^5n^{35}$$  

Multiple Choice

$$6x^5\cdot3x^5\cdot x^0$$  

• $$18x^{10}$$  

• $$9x^{10}$$  

• $$18x^{25}$$  

• $$9x^{25}$$  

Multiple Select

Multiply: 3x(2x³)

• 6x⁴

• 5x³

• 5x⁴

• 6x³

Multiple Select

Multiply: 5a²(7a³- 4a² + a - 2)

• 35a⁵ - 20a⁴ + 5a³ - 10a²

• 12a⁵ - 9a⁴ +5a³ - 7a²

• 35a⁶ -20a⁴ + 5a² - 10

Multiple Choice

Find the product. Simplify your answer.

$$-9\left(-2j^2-j\right)$$  

• $$-11j^2-9j$$  

• $$-11j^2+8j$$  

• $$-18j^2-9j$$  

• $$18j^2+9j$$  

Multiple Choice

Find the product. Simplify your answer.

$$-3h\left(2h^2+3h-3\right)$$  

• $$-6h^2-9h-9$$  

• $$-6h^3-9h^2+9h$$  

Multiple Select

$$\left(x\ +\ 4\right)\left(x\ +\ 8\right)$$  Multiply:

• $$x^2\ +\ 12x\ +\ 32$$  

• $$32x^2$$  

• $$x^2\ +\ 32$$  

Multiple Select

$$\left(2x\ +\ 3\right)\left(3x\ +\ 2\right)$$  

• $$6x^2\ +\ 13x\ +\ 6$$  

• $$6x^2\ +\ 6$$  

• $$5x^2\ +10x\ +5$$  

Multiple Select

$$\left(2x\ -\ 5\right)\left(x\ +\ 4\right)$$  

• $$2x^2\ +3x\ -20$$  

• $$2x^2\ -\ x\ -20$$  

• $$x^2\ -\ 20$$  

• $$x^2\ +\ 13x\ -20$$  

Binomial Squared?

Write the binomial TWICE and multiply (FOIL or Box).

Do NOT square each term!!!

Notice you get a trinomial.

Multiple Choice

Find the product:

$$\left(5s+2\right)^2$$  

• $$25s^2+4$$  

• $$25s^2+10s+4$$

• $$25s^2+20s+4$$  

• $$5s^2+20s+4$$  

Multiple Choice

Find the product. Simplify your answer.

$$\left(6h^2\right)\left(5h^3\right)$$  

• $$11h^6$$  

• $$11h^5$$  

• $$30h^5$$  

• $$30h^6$$  

Multiple Choice

Find the product. Simplify your answer.

$$-9\left(-2j^2-j\right)$$  

• $$-11j^2-9j$$  

• $$-11j^2+8j$$  

• $$-18j^2-9j$$  

• $$18j^2+9j$$  

Multiple Choice

$$\left(2x^2+x+5\right)\cdot\left(x+1\right)$$ Choose the box that represents the situation. 

Multiple Choice

$$\left(2x^2+x+5\right)\cdot\left(x+1\right)$$ Choose the correct equation.

• 2 $$3x^3+2x^2+5x+5$$  

• $$2x^3+3x^2+6x+5$$  

• $$2x^3+2x^2+6x+5$$  

​This video covers dividing a polynomial by a monomial.

Multiple Choice

When I am a dividing by a monomial, I should _______ the coefficients and ________ the exponents for each term.

• add, subtract

• subtract , divide

• divide, divide

• divide, subtract

Multiple Choice

$$\frac{\left(8x^4+6x^3-10x^2\right)}{2x^2}$$  

• $$4x^2+3x-5$$  

• $$4x^2+3x^{1.5}-5x$$  

• $$6x^2+4x-12$$  

• $$6x^2+4x^{1.5}-12x$$  

Multiple Choice

$$\frac{\left(-18x^5-12x^3-6x^2\right)}{-3x}$$  

• $$-15x^4-9x^2-3x$$  

• $$-6x^4-4x^2-2x$$  

• $$6x^4+4x^2+2x$$  

• $$6x^5+4x^3+2x^2$$  

Multiple Choice

$$\frac{81x^9-54x^6+27x^3}{9x}$$  

• $$9x^9-6x^6+3x^3$$  

• $$9x^8-6x^5+3x^2$$  

• $$9x^{10}-6x^7+3x^4$$  

• $$81x^8-6x^5+3x^2$$  

Multiple Choice

$$\left(14d^3-21d^8\right)\div\ 7d^2$$  

• $$7d-21d^6$$  

• $$7d^{1.5}-14d^4$$  

• $$2d-3d^6$$  

• $$2d^{1.5}-3d^4$$