College Math Exponents and Roots

Multiplication vs. Exponents

100

Complete the following equations:

2 xx 3 =

2^3 =

2 xx 3 = 2 + 2 + 2 = 6

2^3 = 2 xx 2 xx 2 = 8

200

4 xx 2 = 

4^2 = 

4 xx 2 = 4 + 4 = 8

4^2 = 4 xx 4 = 16

300

5 xx 2 = 

5^2 = 

5 xx 2 = 5 + 5 = 10

5^2 = 5 xx 5 = 25

400

5 xx 3 = 

5^3 = 

5 xx 3 = 5 + 5 + 5 = 15

5^3 = 5 xx 5 xx 5 = 125

500

2 xx 5 = 

2^5 = 

2 xx 5 = 2 + 2 + 2 + 2 + 2 = 10

2^5 = 2 xx 2 xx 2 xx 2 xx 2 = 32

Rational Exponents

100

Write as an expression with a rational exponent

root(3)((x)^2)

x^(2/3)

200

Write as an expression with a rational exponent.

(root(4)(x))^3

x^(3/4)

300

Write as an expression with a rational exponent.

root(7)(x)

x^(1/7)

400

Write as an expression with a rational exponent.

root(7)(x^10)

x^(10/7)

500

Write as an expression with a positive rational exponent.

root(3)(x^-2)

1/(x^(2/3)

Products of Exponential Expressions

100

Simplify the following expression:

(a^2)(a^5)

a^7

200

Simplify the following expression:

(a^2b^3)(a^5b)

a^7b^4

300

Simplify the following expression:

(3a^4b)(6a^5b)

18a^9b^2

400

Simplify the following expression.  Use only positive exponents in your final answer.

(3a^4b)(a^-6)

(3b)/(a^2)

500

When multiplying like bases, what do you do with the exponents?

add the exponents

Quotients of Exponential Expressions

100

Simplify the following expression:

a^5/a^2

a^3

200

Simplify the following expression, and write your final answer using positive exponents only. 

(a^2)/(a^5)

1/(a^3)

300

Simplify the following expression:

(3a^8)/(a^6)

3a^2

400

When dividing like bases, what do you do with the exponents?

subtract the exponents

500

Simplify the following expression, and write your final answer using positive exponents only. 

(12a)/(6a^5)

2/(a^4)

Powers of Powers

100

Simplify the following expression:

(b^4)^2

b^8

200

Simplify the following expression:

(5b^4c)^2

25b^8c^2

300

Simplify the following expression.  Use only positive exponents in your final answer.

(2b^-4c)^3

(8c^3)/(b^12)

400

When raising a power to a power, what do you do with the exponents?

multiply the exponents

500

Simplify the following expression.  Use only positive exponents in your final answer.

(-2b^-5k)^3

-(8k^3)/b^15

Scientific Notation

100

Convert the following number to scientific notation:

12,300

1.23xx10^4

200

Convert the following number to scientific notation:

0.0005

5xx10^-4

300

Convert the following number to standard form:

-5.32xx10^3

-5320

400

Do the following calculation, and write the answer in scientific notation:

(6xx10^7)(4xx10^5)

2.4xx10^13

500

Do the following calculation, and write the answer in scientific notation:

(32xx10^8)/(2xx10^5)

1.6xx10^4

Square Roots

100

Which of the following numbers is NOT a perfect square?

1, 4, 8, 16, 25, 36

8

200

Simplify the following expression:

sqrt(x^6)

x^3

300

Simplify the following expression:

sqrt(32)

4sqrt2

400

Simplify the following expression:

sqrt(75x^9)

5x^4sqrt(3x)

500

Simplify the following expression:

sqrt(45b^5x^6)

3b^2x^3sqrt(5b)