Exponent Rules and Scientific Notation

Product Rule and Quotient Rule

100

Simplify using Laws of Exponents: c · c⁵

c⁶

200

Simplify using Laws of Exponents:

b^12 / b^8

 

b⁴

300

Simplify using Laws of Exponents: d²² · d^-12

d¹⁰

400

Simplify using Laws of Exponents: x²⁵ / x¹³

x¹²

500

Simplify using Laws of Exponents: 

a^30 / a^-20

a⁵⁰

Power Rule

100

Simplify using Laws of Exponents: (x²)⁵

x¹⁰

200

Simplify using Laws of Exponents: (z³y²)⁵

z¹⁵y¹⁰

300

Simplify using Laws of Exponents: (-x⁴)³

-x¹²

400

Simplify using Laws of Exponents: (-y⁸)⁴

y³²

500

Simplify using Laws of Exponents: (-c²p⁵)¹⁰

c²⁰p⁵⁰

Multiplying and Dividing

100

Simplify using Laws of Exponents:(-2w⁴)(5w)

-10w⁵

200

Simplify using Laws of Exponents: 2x⁹ / 4x⁵

(2x^9) / (4x^5)

x^4 /2 

aka 0.5x⁴

300

Simplify using Laws of Exponents: (6b¹²)(2b²)(b^-5)

4b⁹

400

Simplify usi

(-8r^10) / (2r^-5)

ng Laws of Exponents: -8r¹⁰ / 2r^-5

-4r¹⁵

500

Simplify using Laws of Exponents: (-2sr)³(2s²r³)

-16s⁵r⁶

Power Rule EXTREME

100

Simplify using Laws of Exponents: (5j⁶)⁴

625j²⁴

200

Simplify using Laws of Exponents: (8v⁹)⁵

32768v⁴⁵

300

Simplify using Laws of Exponents: (-3a⁵b^-12)⁵

-243a²⁵/ b⁶⁰

400

Simplify using Laws of Exponents:

(7a^- 5b^6)^4 / (7a^4b)^4

(b^20) / (a^36)

500

Simplify using Laws of Exponents:

(-xy)^5(-3x^-2)^3

 (-xy)⁵ x (-3x^-2)³

(27y^5) / (x)

Scientific Notation

100

What is .000078 in scientific notation?

7.8 x 10^-5

200

What is 6.022 x 10⁴ in standard notation?

60220

300

(8.27 x 10^-4) - (7.8 x 10^-4)

0.47 x 10^-4 
=4.7 x 10^-5

400

(2.5 x 10⁶) + (4.12 x 10⁸)

=(.025 x 10⁸) + (4.12 x 10⁸)

=4.135 x 10⁸

500

(2.5 x 10⁶) x (4.9 x 10^-8)

=12.25 x 10^-2

=1.225 x 10^-1