Indices Review

Multiplying Indices

100

a³ x a²

a⁵

200

2⁵ x 2⁵ x 2^-3

2⁷

300

2e³ x 5e²

10e⁵

400

5m²n¹² x 3m³n⁶ x -2mn²

-30m⁶n²⁰

500

12m²n⁶ x 3m⁸n² x m^-3n^-5

36m⁷n³

Dividing Indices

100

d^11/(d^2)

d⁹

200

28h¹⁰ ÷ 7h⁵

4h⁵

300

16a⁶b³ ÷ 2ab²

8a⁵b

400

10g⁷h⁶ ÷ 2g³h⁴

5g⁴h²

500

(26m^5n^3)/(8m^2 n^5 )

(13m^3)/(4n^2 )

Indices with powers

100

(h³)²

h⁶

200

(2m⁶)⁴

16m²⁴

300

(h^-3)⁵

h^-15

400

(3m³n⁵)³

27m⁹n¹⁵

500

2a³(4ab⁴)³

128a⁶b¹²

Harder Indices

100

a⁶ x b² x a³ x b⁴

a⁹b⁶

200

(2x⁵y³)⁰

1

300

(25x^4×4x^2)/(5x^8) 

20/(x^2)

400

(4x^2y⁶×7x^2y×(2x^3y)³)/(6x^5y⁸×2x^7y⁵)

(56x)/(y^3)

500

(14x^4*(2x^3)^4)/(3x^2)^3

(64x^7)/27

Negative indices

100

Write without negative indices

x^-2

1/(x^2)

200

Write without negative indices

2x^-2

2/(x^2)

300

write without negative indices

3*x^-2y^4z^-3

(3y^4)/(x^2z^3)

400

Write with negative indices

1/(3x^5)

(x^-5)/3

500

Find x  if     4^x = 64

x = 3

Scientific Notation

100

7000

7 x 10³

200

0.006

6 x 10^-3

300

45300

4.53 x 10⁴

400

0.0000095

9.5 x 10^-6

500

123000000000000

1.23 x 10¹⁴

Standard Notation

100

2 x 10³

2000

200

3.8 x 10^-9

0.0000000038

300

4.321 x 10^-5

0.00004321

400

5.2 x 10⁷

52000000

500

6.23 x 10²³

623000000000000000000000