Indices

Laws of Indices

100

What are the rules for positive indices?

When multiplying, add the exponents When dividing, subtract the exponents

200

What is the rule for the zero index?

Anything raised to a 0 is a 1

300

What are the rules for negative indices?

Flip the negative number to the oppside side (find the recipical)

400

What are exponential equations?

Equations that involve indices as unknowns.

500

Are indices considered exponents?

Yes. Ha ha you thought this was a hard one And someone got by with common sense and now they have 500 points Life sucks huh?

Positive Indices

100

simplify 4⁵* 3⁴* 4²

4⁷ * 3⁴

200

Simplify 2⁴*5⁷*5³*6²*6⁸

2⁴*5¹⁰*6¹⁰

300

Simplify 3⁹÷3²

3⁷

400

Simplify 3x⁷y⁵z³÷9x⁴y³z

3x³yz²÷9

500

Simplify 6³*6³*8⁵*8⁶ __________ 8⁶*6²

6⁴*8⁵

Zero Index

100

 2³*2⁰

8

200

 4²*8⁰

16

300

 (4⁰)²

1

400

 4⁰*3² 

_______

6⁰

9

500

4³*3⁷*4-³*3-⁵

9

Negative Indices

100

6³*6-³

1

200

4*2-³

1/2

300

5÷2-²

1 1/4

400

8-⁶÷8-⁴

⅟8² or ⅟64

500

100*10-¹

10

Exponential Equations

100

2^x =4

x=2

200

2^x=16

x=4

300

(⅓)^x =81

X= -4

400

4^-x=⅟₁₆

X=2

500

6^z=36^z

Z=0