Exponent Review

True/False

100

x²*x⁴=x⁸

True

200

x^-4=1/x^-4

False, 1/x⁴

300

4⁰(4⁴)⁷=4¹²

False, 4²⁸

400

x⁰/x^-4=x^0-4

False, it equals x^0-(-4)=x⁴

500

x³x⁶/4³*4¹⁰=x⁹4⁷

True

Simplifying Radicals

100

Simplify root(8)

root(8)=2root(2)

200

Simplifying root(40)

root(40)=2root(10)

300

Simplify 3*root(80)

3*root(80)=3*4root(5)=12root(5)

400

What value of x makes root(5x)=5root(3)

x=15

500

What value makes 2root(51x)=10root(51)?

x=25

Simplifying Expressions

100

Simplify the expression so there are only positive exponents:

(.04x)⁰*6

6

200

Simplify the expression so there are only positive exponents:

5^-5/5^-9

5⁴

300

Simplify the expression so there are only positive exponents:

x⁴y⁶z⁰*x^-5y⁰z¹⁰

xy⁶z¹⁰

400

Simplify the expression so there are only positive exponents:

(3^-2/x⁴)⁵

1/(3¹⁰x²⁰)

500

Simplify the expression so there are only positive exponents:

(x^-4y⁰z²)²*(3¹x²y⁰)^-3

z⁴/(27x¹⁴)

Simplifying Expressions 2

100

Simplify the expression so there are only positive exponents:

(x²)³

x⁶

200

Simplify the expression so there are only positive exponents:

(5²)^-10

1/5²⁰

300

Simplify the expression so there are only positive exponents:

(7⁴)^-3/7^-4

1/7⁸

400

Simplify the expression so there are only positive exponents:

x²y⁰z^-2*x^-2y²z⁷(x²y^-3z⁶)

x²z¹¹/y

500

Simplify the expression so there are only positive exponents:

(x^-2y^-1z^-8)^-2x²y⁰z²(xyz)⁰

x⁶y²z¹⁸

Power Functions

100

What is the degree of x⁵?

5

200

What is the degree of 3⁴5¹⁰⁶x²?

2

300

Which of the following are power functions?

x², x^-2, 5x⁸, x+1

x² and 5x⁸

400

Simplify the following functions, and determine which grows faster and explain why:

f(x)=(x⁴x⁵)²

g(x)=3x⁸/x^-4

f(x)=x¹⁸

g(x)=3x¹²

f(x) grows faster since it has a higher degree

500

Simplify the following functions, and determine which grows faster and explain why:

f(x)= 2x¹⁰x¹⁰*3x⁴

g(x)=(2x⁸x⁰)³

f(x)=8x²⁴

g(x)=6x24

Since both functions have the same degree, g(x) grows faster since it has a bigger coefficient