Indices Year 10 Including Negatives

Laws of Indices

100

What is the rule for multiplying positive indices?

When multiplying, add the exponents. 

200

What is the rule for dividing positive indices?

When dividing, subtract the exponents

300

What is the rule for the zero index?

Anything raised to a 0 is a 1

400

What is the rule for multiplying indices with different bases? 

When multiplying indices with different bases, calculate each exponential term individually

500

Are indices considered exponents?

Yes.

Positive Indices

100

Simplify 4⁵ x 3⁴ x 4²

4⁷ x 3⁴

200

Simplify 2⁴ x 5⁷ x 5³ x 6² x 6⁸

2⁴ x 5¹⁰ x 6¹⁰

300

Simplify 3⁹÷3²

3⁷

400

Solve 3x⁷y⁵ ÷ 3x¹⁰y³

   3y²

^________

     x³

500

Simplify

               a³ x a³ x b⁵ x b⁶

             _______________

                      b⁶ x a²

 a⁴ x b⁵

Zero Index

100

Solve 2³ x 2⁰

8

200

Solve 4² x 8⁰ x 4^-² x 2⁰ 

1

300

What is 9⁴ as a number?

6561

400

Solve

             4⁰ x 4¹⁰

   

4¹⁰

500

Solve 4³ x 4-³

4⁰ = 1

Negative Indices

100

Solve 6³ x 6-³

1

200

Solve 4 x 2-³

1/2

300

a^-5 x a⁴ 

a

400

Solve 8^-⁶÷8^-⁴

1/8² or 1/64

500

Solve 10¹⁰¹ x 10-¹

10¹⁰⁰

Exponential Equations

100

solve for x    2^x =4

x=2

200

 solve for x

2^x=16

x=4

300

7³ =

343

400

4 raised to which number gives us 48

3

500

6^z=36

Z=2