Math Exponents and Roots

Solve

1

-27^(5/3) 

-243

2

4^(5/2) 

32

3

-125^(4/3)

625

4

(64/125)^(-2/3) 

25/16

5

64^(2/3)

16

Rational Exponents

1

Write as an expression with a rational exponent.

root(7)(x^10)

x^(10/7)

2

Write as an expression with a rational exponent.

(root(4)(x))^3

x^(3/4)

3

Write as an expression with a rational exponent.

root(7)(x)

x^(1/7)

4

Write as an expression with a positive rational exponent.

root(3)(x^-2)

1/(x^(2/3)

5

Write as an expression with a rational exponent

root(3)((x)^2)

x^(2/3)

Products of Exponential Expressions

1

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

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

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

2

Simplify the following expression:

(a^(1/2)b^4)(a^(5/4)b^(1/3))

a^(7/4)b^(13/3)

3

Simplify the following expression:

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

18a^9b^2

4

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

add the exponents

5

Simplify the following expression:

(a^2)(a^5)

a^7

Quotients of Exponential Expressions

1

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

subtract the exponents with a common denominator

2

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

(a^(1/2))/(a^(2/5))

a^(1/10)

3

Simplify the following expression:

(3a^(3/8))/(a^(5/6))

3/(a^(11/24))

4

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

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

2a^(4/5)

5

Simplify the following expression:

a^5/a^2

a^3

Powers of Powers

1

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

multiply the exponents

2

Simplify the following expression:

(5b^4c)^2

25b^8c^2

3

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

(2b^-4c)^3

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

4

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

(-2b^-5k)^3

-(8k^3)/b^15

5

Simplify the following expression:

(b^4)^2

b^8

Roots

1

Simplify the following expression:

root(4)(162x^3y^5)

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

2

Simplify the following expression:

sqrt(x^6)

x^3

3

Simplify the following expression:

root(3)(32)

2root(3)4

4

Simplify the following expression:

sqrt(45b^5x^6)

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

5

Which of the following numbers is NOT a perfect square?

1, 4, 8, 16, 25, 36

8

EAGLES (after everything is done)

1

Who won Super Bowl MVP when the Eagles beat the Chiefs in Super Bowl 59?

Jalen Hurts

2

Who won Super Bowl MVP when the Eagles beat the Patriots in Super Bowl 52?

Nick Foles

3

Cooper DeJean scored a pick 6 during Super Bowl 59. What number is his jersey?

33

4

What was the final score when the Eagles beat the Patriots to win Super Bowl 52

41-33

5

What was the final score when the Eagles beat the Chiefs to win Super Bowl 59

40-22