Master Exponents: Enhance Your College Algebra Skills for Nursing

Question 1

Simplify the expression: (2^3)^2

Accepted Answer

2^6

Answer

4^3

Answer

8^3

Answer

16^2

Question 2

Which of the following is equivalent to ((ab)^3)?

Accepted Answer

(a^3)(b^3)

Answer

(a^3 + b^3)

Answer

(a^(3x) + b^(3x))

Answer

(a)(b^3)

Question 3

Evaluate: 3^(-2)

Accepted Answer

(1/9)

Answer

(1/3^2)

Answer

3^2

Answer

(1/3)

Question 4

Which of the following expressions is in simplest radical form?

Accepted Answer

2sqrt(2)

Answer

sqrt(8)

Answer

2sqrt(4)

Answer

4sqrt(2)

Question 5

Evaluate: (3 + 2i)(5 - 4i)

Accepted Answer

11 + 14i

Answer

19 + 2i

Answer

7 - 8i

Answer

-11 + 14i

Question 6

According to the zero exponent property, what is the value of 2^0 - 5^0?

Accepted Answer

0

Answer

-3

Answer

3

Question 7

Find the value of x in the exponential equation 5^x = 25 using the definition of exponents:

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 8

Which property of exponents is illustrated by the equation (ab)^n = a^n * b^n?

Accepted Answer

Power of a Product

Answer

Zero Exponent Property

Answer

Negative Exponent Property

Answer

Power of a Quotient

Question 9

Which of the following is equivalent to the expression 4^(1/2), using the definition of fractional exponents?

Accepted Answer

2

Answer

4

Answer

8

Answer

16

Question 10

Which of the following is NOT a property of exponents?

Accepted Answer

Exponents can be positive integers only

Answer

Product of powers property

Answer

Zero power property

Answer

Quotient of powers property

Question 11

Simplify: (2/3)⁻⁴

Accepted Answer

81/16

Answer

16/81

Answer

81/4

Answer

4/81

Question 12

Which of the following is equivalent to (4¹/²)³?

Accepted Answer

4^(9/2)

Answer

4^(3/2)

Answer

8

Answer

16

Question 13

Evaluate the following: 2^(-3)

Accepted Answer

1/8

Answer

8/1

Answer

-8/1

Question 14

Simplify: (2x^3y^2z)^(-2)

Accepted Answer

1/4x^6y^4z^2

Answer

-4x^6y^4z^2

Answer

4x^6y^4z^2

Answer

-1/4x^6y^4z^2

Question 15

Find the value of: (1/2)^(-2)

Accepted Answer

4

Answer

-2

Answer

-4

Answer

2

Question 16

Find the value of (-3)^-2

Accepted Answer

1/9

Answer

9

Answer

-1/9

Answer

-9

Question 17

Simplify the expression (2^3)^4 using the power of a power property:

Accepted Answer

2^12

Answer

4^3

Answer

2^7

Answer

8^4

Question 18

Evaluate 3^-2 using the negative exponent property:

Accepted Answer

1/9

Answer

9

Answer

1/3

Question 19

Which of the following is equivalent to (x^a)(x^b) using the product of powers property?

Accepted Answer

x^(a+b)

Answer

x^(a-b)

Answer

x^ab

Answer

(x^a)/(x^b)

Question 20

Identify the option that is NOT a valid property of exponents:

Accepted Answer

a^0 = 0

Answer

a^-m = 1/a^m

Answer

(a^m)^n = a^(m*n)

Answer

a^m * a^n = a^(m+n)

Question 21

Simplify the expression (x^2y^3)^-1 using the power of a quotient property:

Accepted Answer

x^-2y^-3

Answer

x^2y^2

Answer

x^-2y^-2

Answer

xy^-3

Question 22

Evaluate (1/2)^-4 using the negative exponent property for rational exponents:

Accepted Answer

16

Answer

1/4

Answer

1/16

Answer

4

Question 23

Solve for x in the radical equation x^(3/4) = 8 using the radical exponent property:

Accepted Answer

16

Answer

8

Answer

32

Answer

4

Question 24

Evaluate the expression (2^-3)^2:

Accepted Answer

1/16

Answer

1/4

Answer

4

Answer

16

Question 25

Find the base 2 logarithm of 128:

Accepted Answer

7

Answer

11

Answer

5

Answer

9

Question 26

Which of the following is equivalent to 5^-2?

Accepted Answer

1/25

Answer

5^2

Answer

25

Answer

-25

Question 27

Which of the following equations is true for all non-zero values of x and y?

Accepted Answer

(x^my^n)^k = x^(mk)y^(nk)

Answer

(x^my^n)^k = x^(m-n)y^(k+n)

Answer

(x^my^n)^k = x^(mk) + y^(nk)

Answer

(x^my^n)^k = x^(m+n)y^(k+n)

Question 28

Evaluate the value of 2^(-3).

Accepted Answer

1/8

Answer

1/4

Answer

-8

Answer

8

Question 29

Multiply the monomials (2x^3y^2) and (3xy^3) and write the product in its simplest form.

Accepted Answer

6x^4y^5

Answer

6x^2y^6

Answer

5x^3y^5

Answer

12x^4y^4

Question 30

Divide the monomial (16x^6y^4) by (4x^2y^2) and express the result in its simplest form.

Accepted Answer

4x^4y^2

Answer

12x^4y^6

Answer

4x^2y^4

Question 31

Simplify the expression (3x^2y^3z)^0.

Accepted Answer

1

Answer

x^2y^3z

Answer

3

Answer

0

Question 32

Simplify the expression: (x^3 / y^2)^-2

Accepted Answer

y^4 / x^6

Answer

x^(-6) / y^(-4)

Answer

x^6 / y^4

Answer

y^(-4) / x^(-6)

Question 33

Solve for x: 27^x = 9

Accepted Answer

1/3

Answer

3

Answer

-3

Answer

1/9