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

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

16/r^2

500

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

(21s^11)/p^2

600

(2/3)^(1/3)*(2/3)^(1/4)

What is 

(2/3)^(7/12)

Power Rule

100

(x^4)^5

x^20

200

4(y^3)^2

4y^6

300

(xy)^6

x^6y^6

400

(4w^5)^2

16w^10

500

(8w^3y^7)^0

1

600

(6x^(1/2)y^(2/3))^(1/5)

What is 

6^(1/5)y^(1/10)x^(2/15)

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

(4m^4)/(8m^8)

1/(2m^4)

600

(2/3)^(1/4)/(2/3)^(1/3)

What is 

1/(2/3)^(1/12)

Negative Exponent Rule

100

Any number to the Zero power is? ___________

The base cannot be 0

What is 1

200

4x^-9

4/(x^9)

300

((x^2y^(-3))/(z^-5w^6))^-2

What is

(w^12y^6)/(z^10x^4)

 

400

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

18/(x^4)

500

(v^5)^-8

1/(v^40)

600

11a^2 * 3a^-6

33/a^4

Radicals <-> Exponents

100

^{Write the expression in radical form in exponent form.}

(root3 x)^2

What is

x^(2/3)

200

^{Write the expression in radical form in exponent form.}

sqrt(x

What is

x^(1/2)

300

^{Write the expression in exponent form in radical form.}

(4y)^(4/5

What is

root5 (4y)^4

400

^{Write the expression in radical form in exponent form.}

rootm (x^n)

What is 

x^(n/m)

500

Write the expression in exponential form

root(3)(4x^7y^2)

What is 

4^(1/3)x^(7/3)y^(2/3)

600

Write the expression in radical form

x^(3/5)y^(1/4)

What is 

root(20)(x^12*y^5) 

Exponent Challenge

100

Solve for x

t^3*t^x=t^9

x = 6

200

Solve for x. 

a^15/a^x=a^5

x = 10

300

Solve for x 

(b^7)^x=b^42

x = 6

400

Solve for x.

g^(3/4)*g^x=g^(6/4)

x= 3/4

500

Solve for x. 

y^x=1/y^3

x = -3

600

Solve for x.

e^x/e^4=e

x = 5