Exponents and Scientific Notation

Product Rule

100

10² * 10¹⁹

10²¹

200

g²⁷ * g^-11

g¹⁶

300

277^-9 * 277⁹

277⁰ OR 1

400

w⁹⁹ * w¹⁰³

w²⁰²

500

Give answer in standard form, without exponents.  Simplify first, then determine final value.

8⁵ * 8⁷ * 8^-10

64

Quotient Rule

100

y¹⁸ / y⁷

y¹¹

200

12¹⁴ / 12

12¹³

300

6⁷ / 6⁷

6⁰  OR 1

400

Give final value of the expression once you have simplified it.

10²⁹ / 10²⁶

1,000

500

m⁷ / m^-3

m¹⁰ (It ends up being 7 - -3 so the negatives cancel and become addition)

Power to Power Rule

100

(f⁴)⁶

f²⁴

200

(9³)¹³

9³⁹

300

(a²b⁷c¹¹)³

a⁶b²¹c³³

400

Write as a standard number after you simplify.

(5³)^-1

1/125

500

True or False:

(10²)³ = 10x10x10x10x10

False, it equals 10 times it else SIX times not 5

Multi-step Exponent Rules

100

(2³*2⁴) / 2⁵

2² or 4

200

Write answer with POSITIVE exponent only.

4^-8 * 4^{6 =} 

1 / 4²  (or 1/16)

300

(10³)⁵ / 10⁷

10⁸

400

True or False:  

(b³)⁴ / b⁶ * b⁶ = b⁰  (or 1)

True

500

Which answer best matches this situation?  3^-2

a.  9

b. -9

c.  1/9

c

Scientific Notation

100

Write 327,000 in scientific notation.

3.27 X 10⁵

200

Write .0000045 in scientific notation.

4.5 X 10^-6

300

Write in standard notation (as normal #):  9.125 X 10⁸

912,500,000

400

Which has a larger value?  4.47 X 10⁵  or 3.38 X 10⁶

Justify your answer by showing or explaining.

3.38 X 10⁶ because it will have an extra place value since the decimal moves 6 places right versus 5

3.38 X 10⁶ because its value will be 3,330,000 and the other will be 447,000

500

Multiply and leave number in scientific notation:

(4 x 10³) (2 x 10⁶)

8 x 10⁹