Exponent Laws

Product of Power

100

x^3*x^9*x^-6

x ⁶

200

3x^5(x^2)^5

3x^15

300

7^-8 * 7^6

1/7^2

400

(12x^2y^-3z^2)*(1/4x^-2y^5z^8)

3y^2z^10

500

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

16/r^2

Quotient of Power

100

(2x^5)/(8x^6)

1/(4x)

200

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

x^6

300

3^0/5^0

1

400

is  equation 1 equivalent to equation 2 (if not what is it equivalent to?)

equation 1:  6x^3y^3

equation 2: (2x^3)(3y^-3)

No. It's equivalent to 

6x^3/y^3

500

Simplify  (x^4x^3y^9)/(x^12y^3) 

y^6/x^5

Power of Power

100

(4x^-4)^-2

x^8/16

200

5x^4y^2(x^2y^3)^4

5x^12y^14

300

(x^4)^-5

1/x^20

400

((4x^6y^4)/(12x^3y^6))^-1

(3y^2)/x^3

500

Simplify 

(2x^-2)^3/(4x^3

2/x^9

Negative Exponents

100

x⁰

1

200

Write the following with positive exponents

(2x^-3y^-1)/(x^-4)

(2x)/y

300

Are the 2 expressions equivalent?  

(6x^-3)/(9y^-1)

(2y)/(3x^3)

yes

400

(15x^5y^-5)(1/5x^-4y^12)

3xy^7

500

500(-1200x)⁰

500

Other

100

Some students were working on a problem and came to this conclusion -- what is the final answer

(a*a*a*b*b*b*b*b*c*d*d)/(a*a*a*a*b*b*c*d)

(b^3d^2)/a

200

When multiplying exponent expressions what happens to the coefficients?  What happens to the exponents?  

You multiply the coefficients and you add the exponents

300

When dividing exponent expressions what happens to the coefficients?  What happens to the exponents?  

You divide the coefficients (simplify and keep in fraction form) and you subtract the exponents.

400

When you raise an exponent expressions to a power  happens to the coefficients?  What happens to the exponents?  

You raise the coefficient to the outside power and you multiply the exponents on the inside by the outside exponent.

500

(x^2x^6y^20)/(x^11y^15)

y^5/x^3