Exponents - 5 Rules

Zero Exponent

100

Anything raised to the ______ power equals one.

Zero

200

9^0=

1

300

5x^0

5

400

7^0 + 3^0 =

2

500

2^0 - 6^0 = 

0

Negative Exponents

100

x^-3=

1/x^3

200

2x^-2 = 

2/x^2

300

1/x^-4= 

x^4

400

(6x^8)/(2x^3)

3x^5

500

(2x^6y^7)/(4x^10y)

y^6/(2x^4)

Product of Powers

100

When multiplying by the same base we ________ the exponents.

Add

200

x^3x^6 = 

x^9

300

x^7x^5x^-2 =

x^10

400

(2x^3)(4x^4) = 

8x^7

500

(-3x^4)(5x^-9) =

-15/x^5

Quotient of Powers

100

When dividing by the same base we _________ the exponents.  

Subtract

200

x^5/x^3

x²

300

(x^9y^7)/x^5

x^4y^7

400

(x^8y^3)/(x^7y)=

xy^2

500

(9x^5y^4)/(3x^3y^3)

3x^2y

Power of Powers

100

When we raise a power to another power, we _________ the exponents.

Multiply

200

(x^2)^4 =

x^8

300

(x^2y^5)^5 =

x^10y^25

400

(xy^4)^3 =

x^3y^12

500

(2x^7y)^3 =

2^3x^21y^3

OR

8x^21y^3