ExplanationWhen dividing powers with the same base, subtract the exponents: 8^15 ÷ 8^14 = 8^(15-14) = 8^1.
2
Between which two consecutive integers does √239 lie?
1 attempt
Medium
Explanation15^2 = 225 and 16^2 = 256, and since 225 < 239 < 256, √239 lies between 15 and 16.
3
What is (1.6 × 10^2) × (5.2 × 10^8) in scientific notation?
Medium
ExplanationMultiply the mantissas (1.6 × 5.2 = 8.32) and add the exponents (2 + 8 = 10), adjusting so the mantissa stays between 1 and 10: 8.32 × 10^10.
4
What is (5.9 × 10^10) ÷ (2.3 × 10^3) in scientific notation?
Medium
ExplanationDivide the mantissas (5.9 ÷ 2.3 ≈ 2.57) and subtract the exponents (10 − 3 = 7), adjusting the mantissa as needed: 2.57 × 10^7.
5
Simplify: 9^9 ÷ 9^8
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 9^9 ÷ 9^8 = 9^(9-8) = 9^1.
6
Simplify: 9^9 ÷ 9^3
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 9^9 ÷ 9^3 = 9^(9-3) = 9^6.
7
Which is greater: 5^3 or 3^6?
Medium
Explanation5^3 = 125 and 3^6 = 729, so 3^6 is greater.
8
Simplify: (4^5)^5
Medium
ExplanationWhen raising a power to another power, multiply the exponents: (4^5)^5 = 4^(5×5) = 4^25.
9
What is 10^2 × 10^6 equal to?
Medium
ExplanationWhen multiplying powers of 10, add the exponents: 10^2 × 10^6 = 10^8.
10
What is 5.9 × 10^6 written as an ordinary number?
Medium
Explanation5.9 × 10^6 means moving the decimal point 6 places to the right, giving 5,900,000.
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11
What is the sign and value of (-4)^4?
Medium
ExplanationSince the exponent 4 is even, (-4)^4 is positive and equals 256.
12
Between which two consecutive integers does √134 lie?
Medium
Explanation11^2 = 121 and 12^2 = 144, and since 121 < 134 < 144, √134 lies between 11 and 12.
13
Which is greater: 4.2 × 10^6 or 6.7 × 10^8?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 6.7 × 10^8 is greater.
14
Express 43,000 in scientific notation.
Medium
ExplanationMove the decimal point so only one nonzero digit remains before it: 43,000 = 4.3 × 10^4.
15
Between which two consecutive integers does √245 lie?
Medium
Explanation15^2 = 225 and 16^2 = 256, and since 225 < 245 < 256, √245 lies between 15 and 16.
16
Simplify: 7^13 ÷ 7^9
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 7^13 ÷ 7^9 = 7^(13-9) = 7^4.
17
Between which two consecutive integers does √243 lie?
Medium
Explanation15^2 = 225 and 16^2 = 256, and since 225 < 243 < 256, √243 lies between 15 and 16.
18
Simplify: 5^7 × 5^8
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 5^7 × 5^8 = 5^(7+8) = 5^15.
19
Which is greater: 4^6 or 4^3?
Medium
Explanation4^6 = 4096 and 4^3 = 64, so 4^6 is greater.
20
Which is greater: 8.4 × 10^5 or 3.3 × 10^3?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 8.4 × 10^5 is greater.
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21
What is (3/7)^3 equal to?
Medium
Explanation(3/7)^3 = 3^3/7^3 = 27/343.
22
What is 7.7 × 10^3 written as an ordinary number?
Medium
Explanation7.7 × 10^3 means moving the decimal point 3 places to the right, giving 7,700.
23
Between which two consecutive integers does √218 lie?
Medium
Explanation14^2 = 196 and 15^2 = 225, and since 196 < 218 < 225, √218 lies between 14 and 15.
24
What is the value of 4^4?
Medium
Explanation4^4 = 4 multiplied by itself 4 times = 256.
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 4.3 × 10^7 is greater.
27
Simplify √12 to its simplest radical form.
Medium
Explanation12 = 2^2 × 3, so √12 = 2√3.
28
Simplify: (3^5)^5
Medium
ExplanationWhen raising a power to another power, multiply the exponents: (3^5)^5 = 3^(5×5) = 3^25.
29
Simplify √248 to its simplest radical form.
Medium
Explanation248 = 2^2 × 62, so √248 = 2√62.
30
What is the value of 5^3?
Medium
Explanation5^3 = 5 multiplied by itself 3 times = 125.
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31
What is (6.0 × 10^2) × (1.5 × 10^6) in scientific notation?
Medium
ExplanationMultiply the mantissas (6.0 × 1.5 = 9.0) and add the exponents (2 + 6 = 8), adjusting so the mantissa stays between 1 and 10: 9.0 × 10^8.
32
What is (9.5 × 10^8) × (9.4 × 10^2) in scientific notation?
Medium
ExplanationMultiply the mantissas (9.5 × 9.4 = 89.3) and add the exponents (8 + 2 = 11), adjusting so the mantissa stays between 1 and 10: 8.93 × 10^11.
33
Simplify: 9^4 × 9^3
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 9^4 × 9^3 = 9^(4+3) = 9^7.
34
Which is greater: 6^6 or 5^6?
Medium
Explanation6^6 = 46656 and 5^6 = 15625, so 6^6 is greater.
35
What is (2.5 × 10^5) × (8.9 × 10^3) in scientific notation?
Medium
ExplanationMultiply the mantissas (2.5 × 8.9 = 22.25) and add the exponents (5 + 3 = 9), adjusting so the mantissa stays between 1 and 10: 2.23 × 10^9.
36
What is (2/9)^4 equal to?
Medium
Explanation(2/9)^4 = 2^4/9^4 = 16/6561.
37
Simplify: (4^4)^5
Medium
ExplanationWhen raising a power to another power, multiply the exponents: (4^4)^5 = 4^(4×5) = 4^20.
38
What is (2.7 × 10^4) × (8.1 × 10^7) in scientific notation?
Medium
ExplanationMultiply the mantissas (2.7 × 8.1 = 21.87) and add the exponents (4 + 7 = 12), adjusting so the mantissa stays between 1 and 10: 2.19 × 10^12.
39
Simplify: 4^8 ÷ 4^4
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 4^8 ÷ 4^4 = 4^(8-4) = 4^4.
40
Express 82,000 in scientific notation.
Medium
ExplanationMove the decimal point so only one nonzero digit remains before it: 82,000 = 8.2 × 10^4.
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41
Simplify: 8^6 × 8^6
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 8^6 × 8^6 = 8^(6+6) = 8^12.
42
Which is greater: 3.2 × 10^3 or 3.1 × 10^4?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 3.1 × 10^4 is greater.
43
Which is greater: 2^2 or 5^6?
Medium
Explanation2^2 = 4 and 5^6 = 15625, so 5^6 is greater.
44
What is (4.2 × 10^8) × (8.6 × 10^7) in scientific notation?
Medium
ExplanationMultiply the mantissas (4.2 × 8.6 = 36.12) and add the exponents (8 + 7 = 16), adjusting so the mantissa stays between 1 and 10: 3.61 × 10^16.
45
What is (4.9 × 10^8) × (7.3 × 10^3) in scientific notation?
Medium
ExplanationMultiply the mantissas (4.9 × 7.3 = 35.77) and add the exponents (8 + 3 = 12), adjusting so the mantissa stays between 1 and 10: 3.58 × 10^12.
46
What is (5.9 × 10^6) ÷ (3.3 × 10^3) in scientific notation?
Medium
ExplanationDivide the mantissas (5.9 ÷ 3.3 ≈ 1.79) and subtract the exponents (6 − 3 = 3), adjusting the mantissa as needed: 1.79 × 10^3.
47
Simplify: 4^11 ÷ 4^10
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 4^11 ÷ 4^10 = 4^(11-10) = 4^1.
48
Simplify: 7^8 ÷ 7^7
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 7^8 ÷ 7^7 = 7^(8-7) = 7^1.
49
Simplify: 6^10 ÷ 6^4
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 6^10 ÷ 6^4 = 6^(10-4) = 6^6.
50
What is 3^-4 equal to?
Medium
ExplanationA negative exponent means take the reciprocal: 3^-4 = 1/3^4 = 1/81.
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51
What is (5/7)^4 equal to?
Medium
Explanation(5/7)^4 = 5^4/7^4 = 625/2401.
52
What is (2.0 × 10^6) ÷ (1.5 × 10^5) in scientific notation?
Medium
ExplanationDivide the mantissas (2.0 ÷ 1.5 ≈ 1.33) and subtract the exponents (6 − 5 = 1), adjusting the mantissa as needed: 1.33 × 10^1.
53
What is (5.7 × 10^7) ÷ (2.7 × 10^4) in scientific notation?
Medium
ExplanationDivide the mantissas (5.7 ÷ 2.7 ≈ 2.11) and subtract the exponents (7 − 4 = 3), adjusting the mantissa as needed: 2.11 × 10^3.
54
What is (6.2 × 10^5) × (2.0 × 10^3) in scientific notation?
Medium
ExplanationMultiply the mantissas (6.2 × 2.0 = 12.4) and add the exponents (5 + 3 = 9), adjusting so the mantissa stays between 1 and 10: 1.24 × 10^9.
55
What is the value of 2^5?
Medium
Explanation2^5 = 2 multiplied by itself 5 times = 32.
56
Between which two consecutive integers does √246 lie?
Medium
Explanation15^2 = 225 and 16^2 = 256, and since 225 < 246 < 256, √246 lies between 15 and 16.
57
What is the cube root of 125?
Medium
Explanation5^3 = 125, so the cube root of 125 is 5.
58
What is 294^0 equal to?
Medium
ExplanationAny nonzero number raised to the power 0 equals 1, by definition.
59
Which is greater: 3^2 or 2^6?
Medium
Explanation3^2 = 9 and 2^6 = 64, so 2^6 is greater.
60
What is (3.0 × 10^7) ÷ (1.8 × 10^6) in scientific notation?
Medium
ExplanationDivide the mantissas (3.0 ÷ 1.8 ≈ 1.67) and subtract the exponents (7 − 6 = 1), adjusting the mantissa as needed: 1.67 × 10^1.
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61
What is (1.5 × 10^8) × (8.2 × 10^4) in scientific notation?
Medium
ExplanationMultiply the mantissas (1.5 × 8.2 = 12.3) and add the exponents (8 + 4 = 13), adjusting so the mantissa stays between 1 and 10: 1.23 × 10^13.
62
Simplify: 4^2 × 4^2
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 4^2 × 4^2 = 4^(2+2) = 4^4.
63
What is 10^4 × 10^9 equal to?
Medium
ExplanationWhen multiplying powers of 10, add the exponents: 10^4 × 10^9 = 10^13.
64
Express 96,000,000 in scientific notation.
Medium
ExplanationMove the decimal point so only one nonzero digit remains before it: 96,000,000 = 9.6 × 10^7.
65
What is 10^7 × 10^1 equal to?
Medium
ExplanationWhen multiplying powers of 10, add the exponents: 10^7 × 10^1 = 10^8.
66
What is (8.4 × 10^6) × (4.9 × 10^5) in scientific notation?
Medium
ExplanationMultiply the mantissas (8.4 × 4.9 = 41.16) and add the exponents (6 + 5 = 12), adjusting so the mantissa stays between 1 and 10: 4.12 × 10^12.
67
What is (8.6 × 10^6) × (6.1 × 10^6) in scientific notation?
Medium
ExplanationMultiply the mantissas (8.6 × 6.1 = 52.46) and add the exponents (6 + 6 = 13), adjusting so the mantissa stays between 1 and 10: 5.25 × 10^13.
68
What is 10^8 × 10^4 equal to?
Medium
ExplanationWhen multiplying powers of 10, add the exponents: 10^8 × 10^4 = 10^12.
69
What is (7/11)^2 equal to?
Medium
Explanation(7/11)^2 = 7^2/11^2 = 49/121.
70
Simplify √450 to its simplest radical form.
Medium
Explanation450 = 15^2 × 2, so √450 = 15√2.
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71
Which is greater: 3^5 or 3^6?
Medium
Explanation3^5 = 243 and 3^6 = 729, so 3^6 is greater.
72
What is 10^5 × 10^1 equal to?
Medium
ExplanationWhen multiplying powers of 10, add the exponents: 10^5 × 10^1 = 10^6.
73
Between which two consecutive integers does √189 lie?
Medium
Explanation13^2 = 169 and 14^2 = 196, and since 169 < 189 < 196, √189 lies between 13 and 14.
74
What is (6.8 × 10^9) ÷ (2.5 × 10^2) in scientific notation?
Medium
ExplanationDivide the mantissas (6.8 ÷ 2.5 ≈ 2.72) and subtract the exponents (9 − 2 = 7), adjusting the mantissa as needed: 2.72 × 10^7.
75
Simplify: 7^8 × 7^7
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 7^8 × 7^7 = 7^(8+7) = 7^15.
76
Between which two consecutive integers does √141 lie?
Medium
Explanation11^2 = 121 and 12^2 = 144, and since 121 < 141 < 144, √141 lies between 11 and 12.
77
Simplify: (3^4)^3
Medium
ExplanationWhen raising a power to another power, multiply the exponents: (3^4)^3 = 3^(4×3) = 3^12.
78
Between which two consecutive integers does √291 lie?
Medium
Explanation17^2 = 289 and 18^2 = 324, and since 289 < 291 < 324, √291 lies between 17 and 18.
79
Which is greater: 5.4 × 10^9 or 2.1 × 10^2?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 5.4 × 10^9 is greater.
80
Which is greater: 3^2 or 3^3?
Medium
Explanation3^2 = 9 and 3^3 = 27, so 3^3 is greater.
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81
What is 159^0 equal to?
Medium
ExplanationAny nonzero number raised to the power 0 equals 1, by definition.
82
What is 673^0 equal to?
Medium
ExplanationAny nonzero number raised to the power 0 equals 1, by definition.
83
What is (2/5)^3 equal to?
Medium
Explanation(2/5)^3 = 2^3/5^3 = 8/125.
84
What is 625^(1/4) equal to?
Medium
Explanation625^(1/4) means the 4-th root of 625, which is 5, since 5^4 = 625.
85
Which is greater: 2^6 or 3^5?
Medium
Explanation2^6 = 64 and 3^5 = 243, so 3^5 is greater.
86
What is 304^0 equal to?
Medium
ExplanationAny nonzero number raised to the power 0 equals 1, by definition.
87
What is (5/9)^2 equal to?
Medium
Explanation(5/9)^2 = 5^2/9^2 = 25/81.
88
Simplify: 8^13 ÷ 8^6
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 8^13 ÷ 8^6 = 8^(13-6) = 8^7.
89
What is (2/5)^3 equal to?
Medium
Explanation(2/5)^3 = 2^3/5^3 = 8/125.
90
Which is greater: 9.7 × 10^5 or 2.8 × 10^9?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 2.8 × 10^9 is greater.
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91
What is (7.9 × 10^5) × (2.2 × 10^7) in scientific notation?
Medium
ExplanationMultiply the mantissas (7.9 × 2.2 = 17.38) and add the exponents (5 + 7 = 13), adjusting so the mantissa stays between 1 and 10: 1.74 × 10^13.
92
What is (4.2 × 10^8) ÷ (3.2 × 10^3) in scientific notation?
Medium
ExplanationDivide the mantissas (4.2 ÷ 3.2 ≈ 1.31) and subtract the exponents (8 − 3 = 5), adjusting the mantissa as needed: 1.31 × 10^5.
93
Which is greater: 3^6 or 4^4?
Medium
Explanation3^6 = 729 and 4^4 = 256, so 3^6 is greater.
94
What is 970^0 equal to?
Medium
ExplanationAny nonzero number raised to the power 0 equals 1, by definition.
95
Express 7,900,000,000 in scientific notation.
Medium
ExplanationMove the decimal point so only one nonzero digit remains before it: 7,900,000,000 = 7.9 × 10^9.
96
What is the value of 2^4?
Medium
Explanation2^4 = 2 multiplied by itself 4 times = 16.
97
Between which two consecutive integers does √218 lie?
Medium
Explanation14^2 = 196 and 15^2 = 225, and since 196 < 218 < 225, √218 lies between 14 and 15.
98
Which is greater: 5.2 × 10^2 or 5.0 × 10^9?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 5.0 × 10^9 is greater.
99
What is (2.0 × 10^6) ÷ (1.5 × 10^4) in scientific notation?
Medium
ExplanationDivide the mantissas (2.0 ÷ 1.5 ≈ 1.33) and subtract the exponents (6 − 4 = 2), adjusting the mantissa as needed: 1.33 × 10^2.
100
What is 6^-3 equal to?
Medium
ExplanationA negative exponent means take the reciprocal: 6^-3 = 1/6^3 = 1/216.