Index Laws - Shepherd

Index Laws 1&2

100

3⁴ x  3⁵

3⁹

200

7⁵/7²

The slash (/) means divide

7³

300

a⁴ x a⁸

a¹²

400

y²w⁵ x y⁴w³

y⁶w⁸

500

12a⁴b³c³ / 6a²bc²

2a²b²c

Index Laws 3&4

100

(5³)⁴

5¹²

200

5⁰

1

300

5(a²)³

5a⁶

400

(m³)⁸ x m³

m²⁷

500

4(a²)³ x (3a)⁰ / 2a²

The slash (/) means divide

2a⁴

Index Laws 5&6

100

(5a²)³

5³a⁶ or 125a⁶

200

(-2a³p²)³

-2³a⁹p⁶ or -8a⁹p⁶

300

(6 / 3)²

4

400

(-2a⁴b³)² / (a²b)²

The slash (/) means divide

4a⁴b⁴

500

((2a²b³c²)⁵ / (a⁴b³c)²) x ((ab²)² / c))

2⁵a⁴b¹³c⁵ or 32a⁴b¹³c⁵

Negative Indices

100

5^-2

1/5²

Slash (/) represents fraction line

200

a^-3

1/a³

Slash (/) represents fraction line

300

5a^-4b⁴

5b⁴ / a⁴

Slash (/) represents fraction line

400

5 / c^-3

Slash (/) represents fraction line

5c³

500

(a^-2 / b^-3)²

Slash (/) represents fraction line

b⁶ / a⁴

Slash (/) represents fraction line

Scientific Notation

100

Write this number in scientific notation

4 500 000

4.5 x 10⁶

200

Write this number in scientific notation

0.0000002

2 x 10^-7

300

Write this as a normal number

4 x 10³

4000

400

Write this as a normal number

3.8 x 10^-5

0.000038

500

Write your solution in scientific notation

(3 x 10⁵) x (4 x 10²)

1.2 x 10⁸