Exponent Rules

Product Rule

100

x^3 * x^6

x^9

200

2x^5 * x^7

2x^12

300

(4f^8)(6f^4)

24f^12

400

(n³)^-2・2n³

2/(n^3)

500

(8r^5)(2r^-7)

16/r^2

600

(7s^5p^5)(3s^6p^-5)

21s¹¹

Power to a Power Rule

100

(x^4)^5

x^20

200

(xy)^6

x^6y^6

300

(4w^5)^2

16w^10

400

4(y^3)^2

4y^6

500

(8w^3y^7)^0

1

600

(k³)² ・ (2k⁴)²

4k¹⁴

Quotient Rule

100

x^7/x^3

x^4

200

(2x^6)/(x^5)

2x

300

(8x^10)/(4x^3)

2x^7

400

u^2/u^9

1/(u^7)

500

(m)/(m^8)

1/(m^7)

600

(2x^3)/(3x^-2)

(2x^5)/(3)

Negative Exponent Rule

100

x^-5

1/(x^5)

200

4x^-9

4/(x^9)

300

(5y^3)/(x^-2)

5x²y³

400

(3x^-8)(6x^4)

18/(x^4)

500

(v^5)^-8

1/(v^40)

600

11a^2 * 3a^-6

33/a^4

Vocabulary

100

Define the Zero Exponent Rule

Any value (known or unknown) to the power of zero is 1

200

Definition of "coefficient"

number that is being multiplied by a variable

Example: in 5x, 5 is the coefficient

300

Definition of "exponent"

The number that tells you how many times to multiply a base value by itself

400

Definition of "product"

the answer to a multiplication problem

500

Definition of "Quotient"

the answer to a division problem

600

Definition of "base":

the number directly before an exponent that is being multiplied by itself

Scientific Notation

100

Why do we use scientific notation?

To represent really big or really small numbers

200

Write 1,250,000,000 in scientific notation

1.25 X 10⁹

300

Write .000000000237 in scientific notation

2.37 X 10^-10

400

Write 1.37 X 10⁷ in standard form.

13,700,000

500

Write 2.46 X 10^-5 in standard form.

.0000246

600

Without using a calculator, which is bigger? 

9.99 X 10^-7 or 1.11 X 10^-6

1.11 X 10^-6 

.00000111 vs. .000000999