Exponents, Radicals, & Scientific Notation

What is the solution of the equation √x − 9 = 8?

2025 October(J08) Math Question 1

2020 June(C02) Math Question 2

2025 October(J08) Math Question 2

2014 April(71H) Math Question 3

2019 December(C03) Math Question 3

3. What is the value of the expression when x = —1 and m = —16 ?

2015 April(73G) Math Question 3

2019 April(B04) Math Question 4

2018 December(B05) Math Question 4

2013 December(71E) Math Question 4

4. For nonzero values of x and y, which of the following expressions is equivalent to — 18x^3y^2 / 3xy?

2015 December(72E) Math Question 4

2019 June(72F) Math Question 4

2013 April(71G) Math Question 5

5. If square root of a = b and b = 9, a=?

2015 December(72E) Math Question 5

2014 June(72C) Math Question 6

2018 December(B05) Math Question 6

7. The number 0.000 000 000 087 3 is equivalent to which of the following expressions?

2015 December(72E) Math Question 7

2013 December(71E) Math Question 8

2011 April(67F) Math Question 8

2010 December(69A) Math Question 8

The expression (x¹⁰)⁴ is equivalent to:

2024 April(Z13) Math Question 8

9. Which of the following is equivalent to (a3)2′ ?

2018 April(A09) Math Question 9

9. Quadrilateral ABCD with vertices A(-2,0), B(0,4), C(5,5), and D(8,2) will be graphed in the standard (x,y) coordinat plane below. Which of the following is a type of quadrilateral determined by these vertices?

2017 December(A10) Math Question 9

2019 April(Z15) Math Question 10

Laws of exponents

2021 April(D05) Math Question 11

13.For all x such that x -:t:0. , which of the following
expressions is equivalent to lSx
2
5
: 25x ?

2019 June(B02) Math Question 13

2020 December(D03) Math Question 13

2010 December(69A) Math Question 14

2014 June(72C) Math Question 14

15. Karen invested $2,000 in a special sayings account.
The balance of this special savings account will double
every 5 years. Assuming that Karen makes no othe:r:
deposits and no withdrawals, what ;will be the balance
of Karen's investment at the end of 40 years?

2019 June(B02) Math Question 15

2012 June(70C) Math Question 15

2009 June(67C) Math Question 15

2014 December(72G) Math Question 15

2019 April(Z15) Math Question 15

16. Which of the following expressions is equivalent to x3 ?

2017 April(74F) Math Question 16

2010 December(69A) Math Question 16

17. A certain computer performs 1.5 x 10^8 calculations per second. How many seconds would it take this computer to perform 6.0 x 10^16 calculations?

2015 April(73G) Math Question 17

Which of the following values is equal to 4√24 − 5√54?

2023 September(G01) Math Question 17

18. In scientific notation, 670,000,000 + 700,000,000 = ?

2014 June(72C) Math Question 18

For all nonzero values of a, the expression (a²a⁴)/a⁶ is equal to:

2024 June(G20) Math Question 18

2021 April(Z04) Math Question 18

20. Which of the following expressions is equivalent to (3x)^2/x^5 ?

2014 June(72C) Math Question 20

2010 April(68G) Math Question 20

2009 December(68A) Math Question 20

2021 June(D06) Math Question 20

2012 April(70G) Math Question 21

21. What value of x makes the equation −1/81 = −3x true?

2021 December(E23) Math Question 21

For a ≠ 0 and any real number n, the expression a^(2n+1) / a^n is equivalent to which of the following?

35 February(Z14) Math Question 21

2012 April(70G) Math Question 22

22. Given u and v such that (a2)1 = a12 and (a')2 = a8 for all positive a, what is au'

2016 December(74H) Math Question 22

For what positive value of a is it true that (√(8a))(√(2a)) = 16?

35 February(Z14) Math Question 22

2012 June(70C) Math Question 23

2017 April(74F) Math Question 25

2009 June(67C) Math Question 25

2019 December(C03) Math Question 25

2009 December(68A) Math Question 26

26. What is the value of √(a2 + b2) when a = √5 and b = √10 ?

2014 April(71H) Math Question 26

2011 April(67F) Math Question 26

2010 December(69A) Math Question 27

27. For all a > 0, which of the following expressions is equal to a-2 ?

2017 June(74C) Math Question 27

2019 December(C03) Math Question 28

'28. Which of the following expressions is equivalent to
~256x 16 ?

2019 June(B02) Math Question 28

2010 June(68C) Math Question 28

2018 December(B05) Math Question 30

30. In a certain country, last year's population was estimated to be 3.6 x 10^6 people, and last year's public debt was estimated to be 1.8 x 10^9 dollars. Based on these estimates, what was last year's public debt per person in this country?

2014 December(72G) Math Question 30

2012 June(70C) Math Question 30

Let n be a positive integer. Which of the following expressions is equivalent to 0.0002ⁿ?

2024 April(Z13) Math Question 30

2018 April(A09) Math Question 31

31. Which of the following expressions is equal to 3 9

2016 December(74H) Math Question 31

31. Given f(x) = x+2 , what is(are) the real value(s) of t for which f(t) = t ?

2017 December(A10) Math Question 31

2012 December(71A) Math Question 31

32. When written in scientific notation, which of the following expressions is equal to the number of blocks used to construct the pyramid?

2016 December(74H) Math Question 32

2012 December(71A) Math Question 32

2020 June(C02) Math Question 32

For all the planets in the solar system, the equation T = 0.4D^1.5 models the relationship between T, the orbital period in Earth days, and D, the average distance in millions of miles from the Sun, given in the table. According to this model, which of the following expressions is equal to Mercury's orbital period in Earth days?

2023 April(F11) Math Question 32

33. Which of the following is equivalent to 82 – 40.5 ?

2017 June(74C) Math Question 33

Which of the following expressions is equal to (2√7 + 1)(√7 − 1) − (√7 − 1)?

2024 September(H11) Math Question 33

2009 December(68A) Math Question 34

2011 June(69F) Math Question 34

35. Which of the following expressions is equivalent to (3 + x)^-100?

2018 June(A11) Math Question 35

Cube Root

Square Root

2021 April(D05) Math Question 35

2015 April(73G) Math Question 36

38. Steve plans to use 28 feet of fencing to enclose a region of his yard for a pen for his pet rabbit. What is the area, in square feet, of the largest rectangular region Steve can enclose?

2017 December(A10) Math Question 38

38. The value of x5(0.5×2+ 2.5x + 6) is between which of the following numbers when x T 10 ?

2018 April(A09) Math Question 38

For all positive values of a and b, 8^(a/b) is equivalent to:

2024 September(H11) Math Question 38

2019 June(72F) Math Question 39

39. When written in scientific notation, the number of rivets used to build the Eiffel Tower is equal to which of the following expressions?

2018 June(A11) Math Question 39

39. The population of American robins in 2015 is equal to 3.2 × 10k for some integer k. What is the value of k ?

2020 December(D03) Math Question 39

Which of the following is equivalent to (x⁴)^(5/4) · (x⁵)^(2/5)?

2024 April(Z13) Math Question 39

Which of the following expressions is NOT equivalent to (4⁹/4¹⁵)^(1/3)?

2024 December(H31) Math Question 39

An investment doubles in worth every 7 years. The worth of this investment was $24,000 exactly 21 years after the investment was made. The worth of the investment exactly 8 years after the investment was made was between:

2023 September(G01) Math Question 40

40. The number a is a positive integer greater than 1. The number b is a negative integer. The number ab is:

2021 April(D05) Math Question 40

2020 July(C01) Math Question 41

A couple is deciding between 2 condos to purchase. Some information about each condo is given below. The couple assumes that the market value of either condo will increase exponentially at a rate of 4% per year.

2021 June(D06) Math Question 41

There were 300 people who paid the early registration fee, 400 people who paid the regular fee, and 300 people who paid the late fee. What is the total revenue from entry fees, in dollars, written in scientific notation?

2023 April(F11) Math Question 41

43. Given that i2 = —1 and that k is a positive integer, what is the value of i (4k + ?

2016 December(74H) Math Question 43

When x, y, and z are positive integers, which of the following relationships will assure that the product x⁰y¹z⁻¹ will have a value greater than 1?

35 February(Z14) Math Question 43

2019 June(B02) Math Question 44

48. Which of the following values is closest to the number of miles between Stars A and D ?

2016 April(73E) Math Question 48

2024 June(G20) Math Question 49

50. A function f(x) is defined as f(x) = 3’2-‘2. What 2 real numbers satisfy f(x) = 1 ?

Exponents, Radicals, & Scientific NotationThere are 130 ACT math questions under Exponents, Radicals, & Scientific Notation

Sub-topics

2025 October(J08) Math Question 1

2020 June(C02) Math Question 2