Exponents, Radicals, & Scientific Notation

Exponent Expressions

2020 June(C02) Math Question 2

2025 October(J08) Math Question 2

2014 April(71H) Math Question 3

2019 December(C03) 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

2018 December(B05) Math Question 6

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

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

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

2010 December(69A) Math Question 16

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

2023 September(G01) Math Question 17

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

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

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

2009 June(67C) Math Question 25

2019 December(C03) Math Question 25

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

2010 June(68C) Math Question 28

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

2012 December(71A) Math Question 31

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

2015 April(73G) Math Question 36

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

2024 September(H11) Math Question 38

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

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

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 ?

2018 April(A09) Math Question 50

2019 April(Z15) Math Question 50

What are the real solutions for the equation x⁴ − 9 = 0?

2024 September(H11) Math Question 50

2019 June(72F) Math Question 51

2009 December(68A) Math Question 51

51. If # represents the operation defined by a # b = a + b^a, then (1 # 2) # 3 =?

2014 April(71H) Math Question 51

2024 April(Z13) Math Question 51

2012 December(71A) Math Question 52

2020 July(C01) Math Question 53

For what real value of x is (3⁷ · 3⁴)/(3⁴)ˣ = 1/9 true?

2024 September(H11) Math Question 53

If (x^y)(x^k) = 1, what relationship must exist between y and k?

2023 April(F11) Math Question 54

56. For all positive real numbers x, which of the following expressions is equivalent to ?

2015 December(72E) Math Question 56

56. For all x > 0, which of the following expressions is NOT equivalent to

2018 June(A11) Math Question 56

56. If a is a positive even integer and b is a positive odd integer, then [(-3)(+3)]^ab is:

2016 April(73E) Math Question 56

What is the value of x in the equation log₃ 54 − log₃ 2 = log₂ x?

2023 September(G01) Math Question 56

57. For how many integers x is the equation 3^(x + 1) = 9^(x-2) true?

2015 April(73G) Math Question 57

2019 December(C03) Math Question 57

2012 June(70C) Math Question 57

58. If x and a are positive rational numbers such that x^2a = 3, then x^6a = ?

2016 April(73E) Math Question 58

2021 June(D06) Math Question 58

2009 April(66F) Math Question 59

60. Let m and n be nonzero real numbers such that 2n+ 1= 2m. Which of the following is an expression for 2 3 in terms of m ?

Exponent ExpressionsExponents, Radicals, & Scientific NotationACT math questions

2020 June(C02) Math Question 2

2025 October(J08) Math Question 2