Exponent Rules, Radicals, Exponential Functions REVIEW

Presentation

•

Mathematics

•

9th Grade

•

Medium

•

CCSS

HSA.APR.A.1, HSF.LE.A.2, 8.EE.A.1

Standards-aligned

Jamie Larson

Used 4+ times

FREE Resource

14 Slides • 23 Questions

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

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

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

Exponent Rules
Simplifying Radicals
Rational Exponents
Operations with Radicals
Exponential Functions

By Jamie Larson

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