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Exponentiation Trivia Quiz

Exponentiation is used in many science applications, such as the calculation of compound interest, radioactive decay and cryptography. How well do you know this mathematical operation? Enjoy!

A multiple-choice quiz by Matthew_07. Estimated time: 4 mins.

Author
Matthew_07

Time
4 mins

Type
Multiple Choice

Quiz #
277,328

Updated
Dec 03 21

# Qns
10

Difficulty
Tough

Avg Score
6 / 10

Plays
458

Question 1 of 10

1. A typical exponentiation operation can be written as x^y (x to the power of y). Here, 'y' is called the exponent. On the other hand, 'x' is called? Hint

The origin

The root

The base

The initial

NEXT>

Question 2 of 10

2. In an exponentiation operation of a^b, b can be either a real number or a complex number.

True

False

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Question 3 of 10

3. Which of the following exponentiation properties is NOT valid? Hint

(b^r)^s = b^(rs)

b^(r+s) = (b^r)x(b^s)

b^(-r) = (-b)^r

b^(r-s) = (b^r)/(b^s)

NEXT>

Question 4 of 10

4. Find the derivative of the function f(x) = p^x, where p is a constant. Hint

xp^(x-1)

p^(x+1)

xp^(x+1)

p^x In p

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Question 5 of 10

5. Generally, a^ (b^c) is equal to (a^b)^c, where a, b and c are any real number constants.

True

False

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Question 6 of 10

6. Which of the following functions is the fundamental function in the study of differential equations? Hint

f(x) = pi ^x (pi = 3.142...)

f(x) = e^x (e = 2.718...)

f(x) = phi ^ x (phi = 1.618...)

f(x) = (surd 2) ^x (surd 2 = square root of 2)

NEXT>

Question 7 of 10

7. The formula e^(ix) = cos x + i sin x provides a convenient way to connect trigonometry and algebra. This formula is known as? Hint

Euler's formula

Fermat's formula

Binet's formula

Newton's formula

NEXT>

Question 8 of 10

8. The equation of x^y = y^x has a unique (only one) solution, namely x = 2, y = 4.

True

False

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Question 9 of 10

9. The expression in the form of a^a^[a^(a^a)] is called... Hint

A power root

A power sum

A power sequence

A power tower

NEXT>

Question 10 of 10

10. The imaginary unit, i (square root of -1) that is raised to the power of ___ will give the solution of 1. Hint

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Quiz Answer Key and Fun Facts

1. A typical exponentiation operation can be written as x^y (x to the power of y). Here, 'y' is called the exponent. On the other hand, 'x' is called?

Answer: The base

The operation x^y (x to the power of y) means that we multiply 'x' for 'y' times. For example, 3^4 means that we multiply the number 3 for 4 times, as in 3 x 3 x 3 x 3 = 81.

2. In an exponentiation operation of a^b, b can be either a real number or a complex number.

Answer: True

The power or the exponent can be a real number or a complex number. For example, 2^2 and 2^(3+4i) are both valid.

3. Which of the following exponentiation properties is NOT valid?

Answer: b^(-r) = (-b)^r

Actually, b^(-r) = (1/b)^r. For example, 3^(-2) = (1/3)^2 = 1/9.

4. Find the derivative of the function f(x) = p^x, where p is a constant.

Answer: p^x In p

For example, if we differentiate the function f(x) = 2^x, we will get 2^x In 2. Notice that if we differentiate x^2, we will get 2x^1 = 2x.

5. Generally, a^ (b^c) is equal to (a^b)^c, where a, b and c are any real number constants.

Answer: False

Let us take an example to prove the equation is incorrect. We take a = 2, b = 3 and c = 4. On the left hand side, we have 2^(3^4) = 2^81. On the right hand side, we have (2^3)^4 = 2^12.

6. Which of the following functions is the fundamental function in the study of differential equations?

Answer: f(x) = e^x (e = 2.718...)

The function f(x) = e^x is called the exponential function. When we differentiate this function, we will get back the function itself, that is dy/dx = e^x. If we integrate this function, we will obtain a family of curves of e^x + c, where c is any real number constant.

7. The formula e^(ix) = cos x + i sin x provides a convenient way to connect trigonometry and algebra. This formula is known as?

Answer: Euler's formula

Euler's formula states that e^(ix) = cos x + i sin x, where e = 2.718..., i is the imaginary unit (square root of 1) and x is the variable. Euler's idea connects the fields of algebra and trigonometry by using complex numbers. A complex number is made up of a real number and a multiple of imaginary units.

For example, 3 + 4i is a complex number, where 3 is the real number, and 4i is a multiple of the imaginary unit.

8. The equation of x^y = y^x has a unique (only one) solution, namely x = 2, y = 4.

Answer: False

Actually, there are many pairs of solutions to the equation of x^y = y^x, which can be solved by using the Lambert W-function.

9. The expression in the form of a^{a^[a^(a^a)]} is called...

Answer: A power tower

For instance, 2^(2^2) = 2^4 = 16. Besides, 3^[3^(3^3)]= 3^(3^9).

10. The imaginary unit, i (square root of -1) that is raised to the power of ___ will give the solution of 1.

Answer: 4

i^0 = 1
i^1 = i
i^ 2 = -1
i^3 = -i
i^4 = 1

Generally, x^0 = 1, where x is any real number.
i^(4y+1) = i
i^(4y+2) = -1
i^(4y+3) = -i
i^(4y+4) = 1
where y is any real number.

Source: Author Matthew_07

This quiz was reviewed by FunTrivia editor crisw before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system.

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