U5 LESSON 3 Algebra with Exponents

​Recall rules of exponents from

ALGEBRA 1​

​

Multiple Choice

$$x^0=$$  

(RECALL Anything raised to a power of zero is always . . .)

• 0

• itself

• 1

• negative

Multiple Choice

Simplify (-9)⁰

• -9

• -1

• 1

• 9

Multiple Choice

$$x^{-1}\ =$$  

(Recall negative exponents are "flipped" to the bottom and made into a denominator)

• $$x^x$$  

• $$-\frac{x}{1}$$  

• $$-\ x$$  

• $$\frac{1}{x}$$  

Multiple Choice

Write an equivalent expression for $$h^{-8}$$ using a positive exponent.

• $$\frac{1}{h^8}$$  

• $$-8h$$  

• $$\frac{8}{h}$$  

• $$h^8$$  

Multiple Choice

Write with positive exponents:

(Remember the negative exponent just gets "flipped" over the line)

• a^-2

• a²

• $$\frac{1}{a^2}$$

• 2a

Multiple Choice

Simplify.  $$2x^{-4}y^3$$  

(remember to "flip" the negative exponent to the bottom)

• $$\frac{2y^3}{x^4}$$  

• $$\frac{x^4}{2y^3}$$  

• $$\frac{y^3}{2x^4}$$  

• $$\frac{2x^4}{y^3}$$  

Multiple Choice

Simplify. $$3x^{-4}y^4$$  

• $$\frac{3y^4}{x^4}$$  

• $$\frac{3y}{x}$$  

• $$\frac{3y^4}{4x}$$  

• $$\frac{4y}{x}$$  

Multiple Choice

Simplify the expression using the rules of exponents.

$$\frac{t^{12}}{t^2}$$  

remember to use subtraction when dividing exponents with the same base

• $$t^{10}$$  

• $$t^{14}$$  

• $$t^{24}$$  

• $$t^6$$  

Multiple Choice

Simplify $$\left(x^8\right)\left(x^{-5}\right)$$  using the rules of exponents

• $$x^{-40}$$  

• $$x^{-13}$$  

• $$x^{13}$$  

• $$x^3$$  

Multiple Select

Simplify: $$\ \left(y^3\right)^{-2}$$  

(Choose two answers)

• $$y^5$$  

• $$y^{-6}$$  

• $$\frac{1}{y^6}$$  

• $$\frac{y^3}{y^2}$$  

Multiple Choice

Simplify the following expression:

(xyz)⁰ =

• 0

• 1

• xyz

• -1

Multiple Choice

(6x²)(-3x⁵)

multiply NUMBERS first and keep them separate!

• 18x⁷

• -18x⁷

• 18x⁷

• 3x⁷

Multiple Choice

Simplify using rules of exponents

(remember to treat the numbers separately)

• $$\frac{\ x^4}{3}$$  

• 3x¹⁰

• 36x¹⁰

• $$\frac{3}{x^4}$$  

Multiple Choice

Simplify $$x^{5\ }\times\ x^7$$   

(from ASVAB test)

• $$x^{12}$$  

• $$x^{35}$$  

• $$35x$$  

• $$12x$$  

Multiple Choice

If $$8^{11}\ =\ 8^9\ \times\ 8^m$$  what is the value of m?

(from ASVAB test)

• 11

• 20

• 9

• 2

Multiple Choice

$$\frac{x^{1-a}}{x^a}=$$  

(from ALEKS test)

• $$x$$  

• $$x^{-a+a^2}$$  

• $$x^{1-2a}$$  

• $$x^{a-1}$$  

• $$x^{1-a^2}$$  

Multiple Choice

ALEKS QUESTION If $$9^x=3^{1-2x}$$   then x =

• $$-\frac{1}{3}$$  

• $$-\frac{1}{4}$$  

• $$\frac{1}{4}$$  

• $$\frac{1}{2}$$