Properties of Exponents

The Product Property

100

Keeping your answer in positive exponents, simplify:

x^(3) * 7y^3

x^(3) * 7y^3

200

Keeping your answer in positive exponents, simplify:

(-4ab^4)(-5a^5b^2)

20a^6b^6

300

Keeping your answer in positive exponents, simplify:

(6x^3y^2)^2

36x^6y^4

400

Keeping your answer in positive exponents, simplify:

2x^(2) * -4x^(4)y^-4

-8x^(6)/y^4

500

Keeping your answer in positive exponents, simplify:

(1/2)(2x^3)^3

4x^9

The Quotient Property

100

Keeping your answer in positive exponents, simplify:

(x^8)/(x^7)

x

200

Keeping your answer in positive exponents, simplify:

(12y^-4)/(3y^-5)

4y

300

Keeping your answer in positive exponents, simplify:

(56mn^4)/(7mn)

8n^3

400

Keeping your answer in positive exponents, simplify:

(-15x^7y^8z^4)/(-45x^3y^5z^3)

(x^4y^3z)/3

500

Keeping your answer in positive exponents, simplify:

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

x^6

Scientific Notation

100

Express in scientific notation 

2,300,000

2.3 * 10^6

200

Express in scientific notation

.0000543

5.43 * 10^-5

300

Solve and write in scientific notation

(1.2 * 10^3)(1.45 * 10^12)

1.74 * 10^15

400

Keeping your answer in positive exponents, simplify:

(5.18 * 10^2)(9.1 * 10^-5)

4.7138 * 10^-2

500

Solve and write in scientific notation and standard form

(1.445 * 10^-7)/(1.7 * 10^5)

8.5 * 10^-13

Negative Exponents

100

Keeping your answer in positive exponents, simplify:

4p^-3

(4)/(p^3)

200

Keeping your answer in positive exponents, simplify:

-6m^-5

-(6)/m^5

300

Keeping your answer in positive exponents, simplify:

-4m^-1

-(4)/(m)

400

Keeping your answer in positive exponents, simplify:

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

(3y^6)/x^3

500

Keeping your answer in positive exponents, simplify:

2k^-1 * (3k^4)^3

54k^11

Rational Exponents

100

Simplify

(343)^(1/3)

7

200

Simplify

(729)^(1/6)

3

300

Keeping your answer in positive exponents, simplify:

(8/27)^(1/3)

2/3

400

Simplify

256^(3/4)

64

500

Simplify

(4/49)^(3/2)

8/343