Master Exponents Rules: Practice Quiz for Mathematical Modelling

Question 1

Simplify the exponential expression: (3^2)^3

Accepted Answer

729

Answer

9

Answer

81

Answer

2187

Question 2

Simplify the expression (2^3)^4:

Accepted Answer

2^12

Answer

8^7

Answer

8^12

Answer

2^7

Question 3

Simplify the expression: sqrt(x^8):

Accepted Answer

x^4

Answer

x^2

Answer

x^8

Answer

1/x^4

Question 4

Simplify the expression: (x^-2 * y^4)^3:

Accepted Answer

x^-6 * y^12

Answer

x^2 * y^-12

Answer

x^6 * y^12

Answer

x^-2 * y^-8

Question 5

Which of the following is equivalent to a^0?

Accepted Answer

1

Answer

a

Answer

0

Answer

-1

Question 6

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

Accepted Answer

1 / 8x^6

Answer

8x^6

Answer

-6x^2

Question 7

Simplify the expression: (a^2b^-3)^4

Accepted Answer

a^8/b^12

Answer

a^6/b^9

Answer

a^2/b^12

Answer

(a^2)^4(b^-3)^4

Question 8

Evaluate: (5^-2)^3

Accepted Answer

1/125

Answer

1/25

Answer

5^6

Answer

5^-6

Question 9

Simplify: (x^2y)^0

Accepted Answer

1

Answer

x^0y^0

Answer

x^2y^2

Question 10

Find the value of x in: x^4 = 16

Accepted Answer

2

Answer

-2

Answer

4

Answer

8

Question 11

Simplify: (x^a)^b

Accepted Answer

x^(a*b)

Answer

x^(a+b)

Answer

x^(a/b)

Answer

x^(b-a)

Question 12

Which of the following is NOT a property of exponents?

Accepted Answer

a^(b+c) = a^b + a^c

Answer

(ab)^c = a^c * b^c

Answer

a^-b = 1/a^b

Answer

a^(b*c) = (a^b)^c

Question 13

Simplify the expression (2³)^⁴.

Accepted Answer

2¹²

Answer

4¹²

Answer

2⁷

Answer

8¹²

Question 14

What is the value of 3⁻²?

Accepted Answer

1/9

Answer

9

Answer

1/3

Answer

-6

Question 15

Simplify the expression (x²y)³ * (x³y²)².

Accepted Answer

x¹¹y⁷

Answer

x⁹y⁵

Answer

x⁵y⁴

Answer

x¹³y⁹

Question 16

Simplify the expression (8⁴ / 2⁶) ÷ 16².

Accepted Answer

1/16

Answer

2

Answer

1/2

Answer

16

Question 17

Simplify the expression (x⁰ * y⁻¹).

Accepted Answer

1/y

Answer

x

Answer

y

Answer

0

Question 18

What is the value of 25½?

Accepted Answer

5

Answer

25

Answer

125

Answer

1/5

Question 19

Simplify (3x²y⁻¹ )³.

Accepted Answer

27x⁶y⁻³

Answer

27x²y⁻³

Answer

9x⁶y⁻³

Answer

9x²y⁻³

Question 20

Which expression is equivalent to 10⁶?

Accepted Answer

(2 x 5)⁶

Answer

(2 + 5)⁶

Answer

6¹⁰

Answer

5¹⁰

Question 21

Simplify (2ᵃ * 2ᵇ)ᶜ.

Accepted Answer

2⁽ᵃ⁺ᵇ⁾ᶜ

Answer

2⁽ᵃ*ᵇ⁾ᶜ

Answer

2ᵃ * 2ᵇᶜ

Answer

2ᵃ + 2ᵇ * c

Question 22

Which of these is NOT a property of exponents?

Accepted Answer

aᵐ + aⁿ = a⁽ᵐ⁺ⁿ⁾ for all a and n

Answer

aᵐ * aⁿ = a⁽ᵐ*ⁿ⁾ for all a and m

Answer

a⁰ = 1 for all nonzero a

Answer

(aᵐ)ⁿ = a⁽ᵐ*ⁿ⁾ for all a and m

Question 23

Simplify: (x^5 * x^3) / x^2

Accepted Answer

x^6

Answer

x^10

Answer

x^5

Answer

x^4

Question 24

Which of the following is equivalent to (a^4)^-2?

Accepted Answer

a^-8

Answer

a^8

Answer

1/a^2

Answer

a^2

Question 25

Express 1/y^5  using a negative exponent.

Accepted Answer

y^-5

Answer

1/y^-5

Answer

y^5

Answer

-y^5

Question 26

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

Accepted Answer

8x^9y^6

Answer

6x^9y^6

Answer

2x^9y^6

Answer

8x^6y^5

Question 27

Evaluate: 5^0 + (1/2)^-1

Accepted Answer

3

Answer

2

Answer

1

Answer

1/2

Question 28

If 2^x = 16, what is the value of x?

Accepted Answer

4

Answer

8

Answer

2

Question 29

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

Accepted Answer

a^3/b^5

Answer

ab

Answer

a^3b

Answer

a/b

Question 30

Express (√x)^3 using fractional exponents.

Accepted Answer

x^(3/2)

Answer

x^3√x

Answer

x^6

Answer

x^(2/3)

Question 31

The population of bacteria doubles every hour. If there were initially 100 bacteria, which expression represents the population after 't' hours?

Accepted Answer

100 * 2^t

Answer

100^t

Answer

100 * t^2

Answer

200 * t

Question 32

Which of the following statements is NOT always true for positive values of 'a' and 'b'?

Accepted Answer

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

Answer

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

Answer

a^-m = 1/a^m

Answer

(a/b)^m = a^m / b^m