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 "base":

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

600

Define the "Product Rule"

a process where you add the exponents when two numbers with the same base are being multiplied together

EOC

100

(x^1/3)³

x

200

(3x²)(x^-2)

3

300

(12x^7)/(4x^5)

3x²

400

(9x^0y^-6)/(z^-2)

9z^2/(y^6)

500

((4xy^-3z)/(2xy))^3

(8z^3)/(y^12)

600

((5a^-2b^-2)/(2abc))^-1

2c/5ab