Rational Exponents and Radicals

Reduce the Rational Exponent

100

64^(2/3)

16

200

4^(5/2) 

32

300

-125^(4/3)

625

400

-27^(5/3) 

-243

500

(64/125)^(-2/3) 

25/16

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

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

add the exponents

200

Simplify the following expression:

(a^(2))(a^(5))

(a^(7))

300

Simplify the following expression:

(a^(1/2)b^(2/3))(a^(1/2)b^(1/3))

ab

400

Simplify the following expression:

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

18a^9b^2

500

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

(3a^(1/3)b)(a^(-2/3))

(3b)/(a^(1/3))

Quotients of Exponential Expressions

100

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

subtract the exponents with a common denominator

200

Simplify the following expression:

(a^(5))/(a^(3))

(a^(2))

300

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

(a^(5))/(a^(6))

1/a

400

Simplify the following expression:

(3a^(3/8))/(a^(1/8))

(3a^(1/4))

500

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

(12a)/(6a^(1/5)

2a^(4/5)

Powers of Powers

100

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

multiply the exponents

200

Simplify the following expression:

(b^4)^2

(b^8)

300

Simplify the following expression:

(5b^4c)^2

25b^8c^2

400

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

(2b^-4c)^3

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

500

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

(-2b^-5k)^3

-(8k^3)/b^15

Perfect Squares/Cubes

100

Which of the following numbers is NOT a perfect square?

1, 4, 8, 16, 25, 36

8

200

What is the square root of 25 plus the square root of 12?

5+2root(2)(3)

300

What are the first 10 perfect squares?

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

400

What is the cube root of 216?

6

500

What is the cube root of -64?

-4

Add/Subtract Radicals

100

When adding and subtracting, what do radicals need to have in common?

They need the same index and radicand

200

Simplify:

−3√5 + 2√5

−√5

300

Simplify:

4root(4)((6))+4root(4)((6))-2root(4)((6))

6root(4)((6))

400

Simplify:

-4root(3)((6))+4root(3)((6))-2root(3)((4))

-2root(3)((4))

500

Simplify:

-3root(4)((6))+4root(3)((6))-2root(2)((4))

-4-3root(4)((6))+4root(3)((6))

Multiply Radicals

100

When multiplying, what do radicals need to have in common?

Radicals need the same index

200

Simplify:

(√2 )(√3)

√6

300

Simplify:

(√8 )(√8)

8

400

Simplify:

(√5x )(√3y)

(√15xy)

500

Simplify:

(4root(4)((3)))(root(4)((3)))(2root(3)((6)))

(8root(4)((9)))(root(3)((6)))