ExplanationWhen dividing powers with the same base, subtract the exponents: 9^11 ÷ 9^6 = 9^(11-6) = 9^5.
2
What is 256^(1/4) equal to?
Medium
Explanation256^(1/4) means the 4-th root of 256, which is 4, since 4^4 = 256.
3
What is 5.9 × 10^8 written as an ordinary number?
Medium
Explanation5.9 × 10^8 means moving the decimal point 8 places to the right, giving 590,000,000.
4
Simplify: 3^12 ÷ 3^11
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 3^12 ÷ 3^11 = 3^(12-11) = 3^1.
5
What is the value of 9^2?
Medium
Explanation9^2 = 9 multiplied by itself 2 times = 81.
6
What is (4.1 × 10^5) × (6.3 × 10^5) in scientific notation?
Medium
ExplanationMultiply the mantissas (4.1 × 6.3 = 25.83) and add the exponents (5 + 5 = 11), adjusting so the mantissa stays between 1 and 10: 2.58 × 10^11.
7
What is (5.1 × 10^7) ÷ (2.9 × 10^2) in scientific notation?
Medium
ExplanationDivide the mantissas (5.1 ÷ 2.9 ≈ 1.76) and subtract the exponents (7 − 2 = 5), adjusting the mantissa as needed: 1.76 × 10^5.
8
What is 9.3 × 10^7 written as an ordinary number?
Medium
Explanation9.3 × 10^7 means moving the decimal point 7 places to the right, giving 93,000,000.
9
What is (5.5 × 10^4) ÷ (4.2 × 10^2) in scientific notation?
Medium
ExplanationDivide the mantissas (5.5 ÷ 4.2 ≈ 1.31) and subtract the exponents (4 − 2 = 2), adjusting the mantissa as needed: 1.31 × 10^2.
10
Simplify: 4^9 ÷ 4^4
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 4^9 ÷ 4^4 = 4^(9-4) = 4^5.
— Sponsored —
11
Simplify: 5^6 × 5^3
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 5^6 × 5^3 = 5^(6+3) = 5^9.
12
What is (7.5 × 10^4) ÷ (3.7 × 10^3) in scientific notation?
Medium
ExplanationDivide the mantissas (7.5 ÷ 3.7 ≈ 2.03) and subtract the exponents (4 − 3 = 1), adjusting the mantissa as needed: 2.03 × 10^1.
13
What is 4.2 × 10^5 written as an ordinary number?
Medium
Explanation4.2 × 10^5 means moving the decimal point 5 places to the right, giving 420,000.
14
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.
15
What is (3.8 × 10^5) ÷ (1.6 × 10^2) in scientific notation?
Medium
ExplanationDivide the mantissas (3.8 ÷ 1.6 ≈ 2.37) and subtract the exponents (5 − 2 = 3), adjusting the mantissa as needed: 2.37 × 10^3.
16
What is (3.2 × 10^5) × (6.7 × 10^3) in scientific notation?
Medium
ExplanationMultiply the mantissas (3.2 × 6.7 = 21.44) and add the exponents (5 + 3 = 9), adjusting so the mantissa stays between 1 and 10: 2.14 × 10^9.
17
What is (7.1 × 10^7) × (7.6 × 10^6) in scientific notation?
Medium
ExplanationMultiply the mantissas (7.1 × 7.6 = 53.96) and add the exponents (7 + 6 = 14), adjusting so the mantissa stays between 1 and 10: 5.4 × 10^14.
18
Simplify: 2^15 ÷ 2^5
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 2^15 ÷ 2^5 = 2^(15-5) = 2^10.
19
Which is greater: 2^6 or 5^5?
Medium
Explanation2^6 = 64 and 5^5 = 3125, so 5^5 is greater.
20
What is (7.2 × 10^7) × (7.1 × 10^6) in scientific notation?
Medium
ExplanationMultiply the mantissas (7.2 × 7.1 = 51.12) and add the exponents (7 + 6 = 14), adjusting so the mantissa stays between 1 and 10: 5.11 × 10^14.
— Sponsored —
21
Which is greater: 7.6 × 10^5 or 7.6 × 10^8?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 7.6 × 10^8 is greater.
22
Which is greater: 4.7 × 10^2 or 6.0 × 10^4?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 6.0 × 10^4 is greater.
23
Simplify: 6^2 × 6^2
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 6^2 × 6^2 = 6^(2+2) = 6^4.
24
What is (8.9 × 10^6) × (4.3 × 10^3) in scientific notation?
Medium
ExplanationMultiply the mantissas (8.9 × 4.3 = 38.27) and add the exponents (6 + 3 = 10), adjusting so the mantissa stays between 1 and 10: 3.83 × 10^10.
25
Which is greater: 7.3 × 10^4 or 2.2 × 10^9?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 2.2 × 10^9 is greater.
26
Between which two consecutive integers does √136 lie?
Medium
Explanation11^2 = 121 and 12^2 = 144, and since 121 < 136 < 144, √136 lies between 11 and 12.
27
What is 343^0 equal to?
Medium
ExplanationAny nonzero number raised to the power 0 equals 1, by definition.
28
Simplify: 9^13 ÷ 9^7
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 9^13 ÷ 9^7 = 9^(13-7) = 9^6.
29
Simplify: (5^5)^5
Medium
ExplanationWhen raising a power to another power, multiply the exponents: (5^5)^5 = 5^(5×5) = 5^25.
30
What is the cube root of 216?
Medium
Explanation6^3 = 216, so the cube root of 216 is 6.
What is (2.7 × 10^5) ÷ (1.1 × 10^2) in scientific notation?
Medium
ExplanationDivide the mantissas (2.7 ÷ 1.1 ≈ 2.45) and subtract the exponents (5 − 2 = 3), adjusting the mantissa as needed: 2.45 × 10^3.
33
Simplify: 9^13 ÷ 9^7
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 9^13 ÷ 9^7 = 9^(13-7) = 9^6.
34
What is the 5th root of 1024?
Medium
Explanation4^5 = 1024, so the 5th root of 1024 is 4.
35
Simplify: (8^4)^3
Medium
ExplanationWhen raising a power to another power, multiply the exponents: (8^4)^3 = 8^(4×3) = 8^12.
36
What is the cube root of 125?
Medium
Explanation5^3 = 125, so the cube root of 125 is 5.
37
Simplify: 3^13 ÷ 3^2
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 3^13 ÷ 3^2 = 3^(13-2) = 3^11.
38
What is (6.8 × 10^7) ÷ (4.3 × 10^3) in scientific notation?
Medium
ExplanationDivide the mantissas (6.8 ÷ 4.3 ≈ 1.58) and subtract the exponents (7 − 3 = 4), adjusting the mantissa as needed: 1.58 × 10^4.
39
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.
40
Which is greater: 2^3 or 6^2?
Medium
Explanation2^3 = 8 and 6^2 = 36, so 6^2 is greater.
— Sponsored —
41
What is the value of (3 × 7)^2?
Medium
Explanation(3 × 7)^2 = 3^2 × 7^2 = 9 × 49 = 441.
42
What is 1.8 × 10^4 written as an ordinary number?
Medium
Explanation1.8 × 10^4 means moving the decimal point 4 places to the right, giving 18,000.
43
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.
44
√8 × √11 is equivalent to which of the following?
Medium
ExplanationBy the product rule for radicals, √a × √b = √(ab), so √8 × √11 = √88.
45
Which is greater: 3^2 or 4^2?
Medium
Explanation3^2 = 9 and 4^2 = 16, so 4^2 is greater.
46
Simplify: 6^7 ÷ 6^5
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 6^7 ÷ 6^5 = 6^(7-5) = 6^2.
47
Simplify: (4^2)^5
Medium
ExplanationWhen raising a power to another power, multiply the exponents: (4^2)^5 = 4^(2×5) = 4^10.
48
Between which two consecutive integers does √68 lie?
Medium
Explanation8^2 = 64 and 9^2 = 81, and since 64 < 68 < 81, √68 lies between 8 and 9.
49
What is 3.6 × 10^6 written as an ordinary number?
Medium
Explanation3.6 × 10^6 means moving the decimal point 6 places to the right, giving 3,600,000.
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 4.9 × 10^9 is greater.
52
What is (7.5 × 10^6) ÷ (4.3 × 10^3) in scientific notation?
Medium
ExplanationDivide the mantissas (7.5 ÷ 4.3 ≈ 1.74) and subtract the exponents (6 − 3 = 3), adjusting the mantissa as needed: 1.74 × 10^3.
53
What is the cube root of 64?
Medium
Explanation4^3 = 64, so the cube root of 64 is 4.
54
What is (9.0 × 10^2) × (7.9 × 10^7) in scientific notation?
Medium
ExplanationMultiply the mantissas (9.0 × 7.9 = 71.1) and add the exponents (2 + 7 = 10), adjusting so the mantissa stays between 1 and 10: 7.11 × 10^10.
55
Which is greater: 8.6 × 10^2 or 9.0 × 10^7?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 9.0 × 10^7 is greater.
56
Simplify: 7^5 × 7^4
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 7^5 × 7^4 = 7^(5+4) = 7^9.
57
What is 10^1 × 10^3 equal to?
Medium
ExplanationWhen multiplying powers of 10, add the exponents: 10^1 × 10^3 = 10^4.
58
What is (9.0 × 10^7) × (4.5 × 10^7) in scientific notation?
Medium
ExplanationMultiply the mantissas (9.0 × 4.5 = 40.5) and add the exponents (7 + 7 = 15), adjusting so the mantissa stays between 1 and 10: 4.05 × 10^15.
59
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.
60
What is 2^-2 equal to?
Medium
ExplanationA negative exponent means take the reciprocal: 2^-2 = 1/2^2 = 1/4.
— Sponsored —
61
Express 440,000 in scientific notation.
Medium
ExplanationMove the decimal point so only one nonzero digit remains before it: 440,000 = 4.4 × 10^5.
62
Simplify: 7^5 × 7^8
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 7^5 × 7^8 = 7^(5+8) = 7^13.
63
What is 6.1 × 10^3 written as an ordinary number?
Medium
Explanation6.1 × 10^3 means moving the decimal point 3 places to the right, giving 6,100.
64
Which is greater: 8.2 × 10^7 or 7.2 × 10^5?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 8.2 × 10^7 is greater.
65
What is the square root of 25?
Medium
Explanation5^2 = 25, so the square root of 25 is 5.
66
What is the square root of 16?
Medium
Explanation4^2 = 16, so the square root of 16 is 4.
67
What is (1.7 × 10^8) × (8.3 × 10^8) in scientific notation?
Medium
ExplanationMultiply the mantissas (1.7 × 8.3 = 14.11) and add the exponents (8 + 8 = 17), adjusting so the mantissa stays between 1 and 10: 1.41 × 10^17.
68
Simplify: (2^3)^3
Medium
ExplanationWhen raising a power to another power, multiply the exponents: (2^3)^3 = 2^(3×3) = 2^9.
69
Which is greater: 4^5 or 5^4?
Medium
Explanation4^5 = 1024 and 5^4 = 625, so 4^5 is greater.
70
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.
— Sponsored —
71
Simplify: 4^2 × 4^4
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 4^2 × 4^4 = 4^(2+4) = 4^6.
72
Express 7,300 in scientific notation.
Medium
ExplanationMove the decimal point so only one nonzero digit remains before it: 7,300 = 7.3 × 10^3.
73
What is (2.6 × 10^5) × (9.8 × 10^5) in scientific notation?
Medium
ExplanationMultiply the mantissas (2.6 × 9.8 = 25.48) and add the exponents (5 + 5 = 11), adjusting so the mantissa stays between 1 and 10: 2.55 × 10^11.
74
What is (7.9 × 10^6) ÷ (2.9 × 10^2) in scientific notation?
Medium
ExplanationDivide the mantissas (7.9 ÷ 2.9 ≈ 2.72) and subtract the exponents (6 − 2 = 4), adjusting the mantissa as needed: 2.72 × 10^4.
75
Which is greater: 3.9 × 10^8 or 5.7 × 10^9?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 5.7 × 10^9 is greater.
76
What is (2.7 × 10^6) × (5.9 × 10^8) in scientific notation?
Medium
ExplanationMultiply the mantissas (2.7 × 5.9 = 15.93) and add the exponents (6 + 8 = 15), adjusting so the mantissa stays between 1 and 10: 1.59 × 10^15.
77
Express 1,200 in scientific notation.
Medium
ExplanationMove the decimal point so only one nonzero digit remains before it: 1,200 = 1.2 × 10^3.
78
Simplify: 3^7 × 3^4
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 3^7 × 3^4 = 3^(7+4) = 3^11.
79
What is 10^3 × 10^1 equal to?
Medium
ExplanationWhen multiplying powers of 10, add the exponents: 10^3 × 10^1 = 10^4.
80
Simplify: 7^4 × 7^3
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 7^4 × 7^3 = 7^(4+3) = 7^7.
— Sponsored —
81
What is (6.8 × 10^7) ÷ (4.2 × 10^3) in scientific notation?
Medium
ExplanationDivide the mantissas (6.8 ÷ 4.2 ≈ 1.62) and subtract the exponents (7 − 3 = 4), adjusting the mantissa as needed: 1.62 × 10^4.
82
Simplify: 5^5 × 5^2
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 5^5 × 5^2 = 5^(5+2) = 5^7.
83
Express 84,000,000 in scientific notation.
Medium
ExplanationMove the decimal point so only one nonzero digit remains before it: 84,000,000 = 8.4 × 10^7.
84
√5 × √3 is equivalent to which of the following?
Medium
ExplanationBy the product rule for radicals, √a × √b = √(ab), so √5 × √3 = √15.
85
What is (9/17)^3 equal to?
Medium
Explanation(9/17)^3 = 9^3/17^3 = 729/4913.
86
Simplify: 5^13 ÷ 5^12
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 5^13 ÷ 5^12 = 5^(13-12) = 5^1.
87
Simplify: (2^3)^5
Medium
ExplanationWhen raising a power to another power, multiply the exponents: (2^3)^5 = 2^(3×5) = 2^15.
88
√3 × √5 is equivalent to which of the following?
Medium
ExplanationBy the product rule for radicals, √a × √b = √(ab), so √3 × √5 = √15.
89
Express 6,000,000,000 in scientific notation.
Medium
ExplanationMove the decimal point so only one nonzero digit remains before it: 6,000,000,000 = 6.0 × 10^9.
90
Which is greater: 9.6 × 10^8 or 8.1 × 10^6?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 9.6 × 10^8 is greater.
— Sponsored —
91
Which is greater: 9.2 × 10^4 or 4.6 × 10^7?
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 4.6 × 10^7 is greater.
92
What is (8.9 × 10^8) × (5.1 × 10^6) in scientific notation?
Medium
ExplanationMultiply the mantissas (8.9 × 5.1 = 45.39) and add the exponents (8 + 6 = 15), adjusting so the mantissa stays between 1 and 10: 4.54 × 10^15.
93
Simplify: 3^9 ÷ 3^6
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 3^9 ÷ 3^6 = 3^(9-6) = 3^3.
94
What is the value of (7 × 2)^2?
Medium
Explanation(7 × 2)^2 = 7^2 × 2^2 = 49 × 4 = 196.
95
Which is greater: 6^6 or 3^6?
Medium
Explanation6^6 = 46656 and 3^6 = 729, so 6^6 is greater.
96
Express 229,999 in scientific notation.
Medium
ExplanationMove the decimal point so only one nonzero digit remains before it: 229,999 = 2.3 × 10^5.
97
Simplify √492 to its simplest radical form.
Medium
Explanation492 = 2^2 × 123, so √492 = 2√123.
98
Simplify √363 to its simplest radical form.
Medium
Explanation363 = 11^2 × 3, so √363 = 11√3.
99
Simplify: 4^8 × 4^3
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 4^8 × 4^3 = 4^(8+3) = 4^11.
100
What is 6.1 × 10^3 written as an ordinary number?
Medium
Explanation6.1 × 10^3 means moving the decimal point 3 places to the right, giving 6,100.