Properties of Exponents

Zero Exponent Property

Negative Exponent Property

Product Of Powers
Power of Products
Power of a Power
Quotient of Powers

Review

Random

100

What is the rule for the Zero Exponent Property?

$a^0 = 1$

$a!= 0$

100

What is the rule for the Negative Exponent Property?

$a^-n = 1/a^n$

100

What is the rule for the product of powers?

What is the rule for the power of products?

product of powers

$a^m + a^n = a^(m+n)$

power of products

$a^n * b^n = (a*b)^n$

100

On a road trip you drove from the Grand Canyon to Yosemite National park, 750 miles, in 12 hours. Then from Yosemite to Zion National park, 480, in 7 hours. Then from Zion to Olympic National park, 1000 miles, in 18 hours. What stretch of the trip were you travelling the fastest?

G.C --> Yosemite = 62.5 M.P.H.

Yosemite --> Zion = 68.57 M.P.H.

Zion --> Olympic = 55.55 M.P.H

You traveled the fastest from Yosemite to Zion.

100

Which famous artist painted the "Starry Night"?
a) Claude Monet
b) Pablo Picasso
c) Vincent van Gogh
d) Leonardo da Vinci

Vincent van Gogh

200

Use the quotient of powers to prove that any number to the zero power equals 1.

Create your own example!

$x^3/x^3 = x^(3-3) = x ^0 = 1$

200

Use the quotient of powers to prove the negative exponent rule?

Create your own example. Write out your expression in expanded form. !

$t^5/t^7 = (t*t*t*t*t)/(t*t*t*t*t*t*t)= 1/t^2$

$t^5/t^7 = t^(5-7) = t^-2 = 1/t^2$

200

What is the rule for the Property of Power of Powers?

What is the rule for the Property of Quotient of Powers?

Power of Powers

$(a^m)^n= a^(m*n)$

Quotient of Powers

$a^m/a^n= a^(m-n)$

200

Solve the following inequality.

$-8(x + 2) > 44$

$-8x - 16 > 44$

$-8x > 60$

$x < -7.5$

200

What is the name of the bounty hunter who captures Han Solo in "The Empire Strikes Back"?
a) Jango Fett
b) Boba Fett
c) Greedo
d) Dengar

Boba Fett

300

Use consistency in patterns prove that anything to the zero power equals 1?

Teacher judged

300

Rewrite each exponent using the negative exponent porperty.

$1/t^6 =$

$1/x^-5$

$x^-3$

$1/t^6 =t^-6$

$1/x^-5 = x^5$

$x^-3 = 1/x^3$

300

Which expressions are equivalent to

$3^2 * 9 ^2$

$3^2 * (3^2)^2$

$27^2$

$27^4$

$12^2$

$3^2 * (3^2)^2$

$27^2$

300

A cube has 6 faces that have a total surface area of 864 units squared. What is the volume of the cube.

$864/6 = 144$

Each face has an area of 144 units squared.

$sqrt144=12$

The side length is 12.

$12^3 =1728$

The total volume is 1728 units cubed.

300

What are the names of Mr. Greenbaums dogs?

Ziggy and Zuzu

400

$y^0 * y^0 + 8 =$

$y^0 * y^0 + 8 = 9$

400

Solve

$4^-2 * 3^-2 * 12^2$

$4^-2 * 3^-2 * 12^2 = 1$

400

Generate 4 expressions equal to

$(x^12/x^4) * x^12$

Teacher judged

400

Is the table proportional? If yes, what is the constant of proportionality. If no, what is one cell you could change to make it proportional?

No. Change the 30 to 40.

400

What is the name of the largest moon of Saturn?
a) Europa
b) Ganymede
c) Io
d) Titan

Titan