Exponent Rules, Radicals, Exponential Functions REVIEW

Exponent Rules
Simplifying Radicals
Rational Exponents
Operations with Radicals
Exponential Functions

By Jamie Larson

Exponent Rules

Learning and Practicing Exponent Rules

Multiple Choice

Simplify

(2a²b⁴z)(6a³b²z⁵)

• 8a⁵b⁶z⁶

• 12a⁶b⁸z⁵

• 12a⁵b⁶z⁶

• 8a⁶b⁸z⁵

Multiple Choice

• 2 / x²

• -2x²

• 2x²

• 2x¹⁴

Multiple Choice

(2⁸)²

• 2¹⁶

• 2¹⁰

• 2⁶

• 2⁴

Multiple Choice

$$\left(4xy^3\right)^3$$  

• $$x^3y^9$$  

• $$64x^3y^9$$  

• $$12x^4y^6$$  

• $$64x^4y^6$$  

Multiple Choice

Simplify the following: $$\left(\frac{x^2}{y^3}\right)^4$$  

• $$\frac{x^8}{y^{12}}$$  

• $$\frac{x^6}{y^7}$$  

• $$x^8y^{12}$$  

Multiple Choice

Simplify:  $$x^{-4}=$$  

• $$\frac{1}{-x^4}$$  

• $$-x^4$$  

• $$\frac{1}{x^4}$$  

• $$\left(-x\right)^4$$  

Multiple Choice

Simplify

• $$\frac{1}{5x^3}$$

• $$\frac{1}{x^5}$$

• $$\frac{-5}{x^3}$$

• $$\frac{5}{x^3}$$

Multiple Choice

Simplify (-9)⁰

• -9

• -1

• 1

• 9

Exponent Rules

• Multiple rules can be used in one problem

• Your final answer should be in the simplest form

• Rules can be used in different orders as well

• Powers must be positive to be fully simplified.

Multiple Choice

Write the following expression in radical form:

• a.)
• b.)
• c.)
• d.)

Multiple Choice

Rewrite as a rational exponent:

$$\sqrt[7]{x^{23}}$$  

• $$x^{\frac{23}{7}}$$  

• $$x^{\frac{7}{23}}$$  

• $$x^{16}$$  

• $$x^{161}$$  

Multiple Choice

Simplify the following radical: √32

• 3√2
• 4√8
• 16√2
• 4√2

Multiple Choice

Simplify the following radical: √80

• 16√5
• 2√20
• 4√5
• 8√5

​Operations with Radicals

Multiple Choice

Simplify

• √5
• -3√6
• √6
• 6

Multiple Choice

Simplify the following:

$$\frac{\sqrt{18}}{\sqrt{3}}$$  

• $$\sqrt{54}$$  

• $$\sqrt{21}$$  

• $$\sqrt{6}$$  

• $$\sqrt{15}$$  

Multiple Choice

Simplify 
3√6 - 4√6

• -√6
• √6
• -1
• Already simplified 

Multiple Choice

Simplify 
-3√20 - √5

• -4√5
• -4√15
• -7√5
• Already simplified 

Exponential Functions have a variable in the exponent

​When x is the exponent, you have an exponential function!!

​b > 1
growth

​0 < b < 1
decay

• ​b is 1 + rate of change
  

• when b > 1 the rate is positive, meaning growth
  

• when 0 < b < 1 the rate is negative, meaning decay

Multiple Select

Which of the following are exponential functions?

• f(x)=4(2)^x

• y=4x²

• y=5^x

• f(x)=3x⁴

Exponential

Growth vs. Decay

If b > 1 then we have growth

If b is a positive fraction (less than 1 but greater than 0) then we have decay

Both Graphs have a

Horizontal Asymptote

(graph never touches

the x-axis)

b^x cannot equal 0

Exponential

What is the value of x when we are on the y-axis? x = 0 on the y-axis


If we want the y-intercept, we would replace x in our equation with 0.

b⁰ = ?

y = b⁰ = 1 (when x is 0, y is 1)
so the y-intercept is at (0,1)

Multiple Choice

The y-intercept for any function in the form

y=b^x

• (0,0)

• (0,1)

• (1,0)

Multiple Choice

What is the y-intercept of f(x)=5(3)^x

• (0,5)

• (0,3)

• (3,0)

• (5,0)

Multiple Choice

Which exponential function represents this graph?

• s(x) = 3^x

• t(x) = 4^x

• k(x) = 5^x

• v(x) = 6^x

Multiple Choice

Which exponential function represents this graph?

• s(x) = 3^x

• t(x) = 4^x

• k(x) = 5^x

• v(x) = 6^x

Multiple Choice

Which exponential function represents this graph?

• s(x) = 3^x

• t(x) = 2(1/3)^x

• k(x) = 5^x

• v(x) = 1/3(2)^x

Multiple Choice

Which exponential function represents this graph?

• s(x) = 3^x

• t(x) = 2(1/3)^x

• k(x) = 5^x

• v(x) = (1/3)^x

REVIEW your notes and assignments for quiz tomorrow