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Quiz about Exponentiation
Quiz about Exponentiation

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.
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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


Question 2 of 10
2. In an exponentiation operation of a^b, b can be either a real number or a complex number.


Question 3 of 10
3. Which of the following exponentiation properties is NOT valid? Hint


Question 4 of 10
4. Find the derivative of the function f(x) = p^x, where p is a constant. Hint


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.


Question 6 of 10
6. Which of the following functions is the fundamental function in the study of differential equations? Hint


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


Question 8 of 10
8. The equation of x^y = y^x has a unique (only one) solution, namely x = 2, y = 4.


Question 9 of 10
9. The expression in the form of a^a^[a^(a^a)] is called... Hint


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.
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