Indices

Notation and Zero index

100

3 x 3 x 3 x 3 x 3 written in index form is 

3⁵

200

The zero index law states that anything to the power of __ is equal to __

0 , 1

300

10⁴ in expanded form is 

10 x 10 x 10 x 10

400

(532141912 x 12314151)⁰ is equal too?

1

500

((5³)⁴)⁰ is equal too ?

1

Adding

100

When attempting to simply an equation involving indices I must first ensure

The bases are the same

200

Given the equation a² x a³ given the ____ are the same i can now ____ my ____

bases, add, indices/powers

300

The solution of a⁵ x a³ is 

a⁸

400

Simplify b⁴ x c⁷ x c³

b⁴c¹⁰

500

z⁷ x g⁶ x u⁵ x g⁴ x u² x z¹¹ simplified is 

g¹⁰u⁷z¹⁸

Subtracting

100

When attempting to simply an equation involving indices I must first ensure

The bases are the same

200

Given the equation a⁵/b³ because the ____ are _____ this equation is already _____

bases, different, simplified/solved

300

The solution of a⁵/a¹ is 

a⁴

400

Simplify a⁷m⁴ / t²m³

a⁷m / t²

500

t²y⁷2⁵ divided by t⁵y³2² simplified is 

8t^-3y⁴

Negative Indices

100

1 / 3⁶ written in expanded form is

1/ 3 x 3 x 3 x 3 x 3 x 3

200

True or False, 3^-6 is the same as (-3 x -3 x -3 x -3 x -3 x -3) 

False

300

Manipulating 1/ 2^-3 and solving gives

2³ = 8

400

Express the following with all indices positive for 3a^-2b⁴ 

3b⁴/a²

500

Express the following with positive indices and then solve for a whole number. 4^-3/8^-2

8²/4³ = 64/64 = 1

Power of a power

100

Given the equation (a^b)^c, the power of power rule states I need to _____ b and c

Multiply

200

Write (2³)² in expanded form

2 x 2 x 2 x 2 x 2 x 2 

300

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2  (12 2's) can be written in the form (2^a)^b with many solutions for a and b find one

(2¹²)¹ or (2⁶)² or (2³)⁴ or (2⁴)³ 

400

(3x⁴)⁰ x (4²)² simplified is 

256

500

Simplify this power of a power equation (2³)⁵/2¹³ to a whole number

2² = 4