Exponents
40 Questions
3 IXL Skills
🎨 Pedagogical Dimensions
Switch between different teaching approaches for this topic.
#1
Level 1
What does 3^2 mean?
Explanation: 3^2 means 3 multiplied by itself, which is 3 x 3 = 9.
#2
Level 1
Calculate 2^3.
Explanation: 2^3 means 2 x 2 x 2 = 8.
#3
Level 1
What is 5^1?
Explanation: Any number raised to the power of 1 is the number itself, so 5^1 = 5.
#4
Level 1
What does 4^2 equal?
Explanation: 4^2 means 4 x 4 = 16.
#5
Level 1
If a pencil costs 2^3 rupees, how much is it?
Explanation: 2^3 means 2 x 2 x 2 = 8.
#6
Level 1
What is 1^5?
Explanation: Any number raised to the power of 0 is 1, so 1^5 = 1.
#7
Level 1
Calculate 2^0.
Explanation: Any non-zero number raised to the power of 0 is 1.
#8
Level 1
What is 10^2?
Explanation: 10^2 means 10 x 10 = 100.
#9
Level 1
If a cricket bat costs 3^2 rupees, how much is it?
Explanation: 3^2 means 3 x 3 = 9.
#10
Level 1
What does 6^1 equal?
Explanation: Any number raised to the power of 1 is the number itself, so 6^1 = 6.
#11
Level 2
Calculate 2^2 + 3^2.
Explanation: 2^2 = 4 and 3^2 = 9, so 4 + 9 = 13.
#12
Level 2
What is (2^3) + (2^2)?
Explanation: 2^3 = 8 and 2^2 = 4, so 8 + 4 = 12.
#13
Level 2
If 5^2 = 25, what is 5^2 + 5^1?
Explanation: 5^1 = 5, so 25 + 5 = 30.
#14
Level 2
Calculate 3^2 - 2^2.
Explanation: 3^2 = 9 and 2^2 = 4, so 9 - 4 = 5.
#15
Level 2
What is (4^1) + (4^2)?
Explanation: 4^1 = 4 and 4^2 = 16, so 4 + 16 = 20.
#16
Level 2
If 2^3 = 8, calculate 2^3 * 2^2.
Explanation: 2^3 * 2^2 = 2^(3+2) = 2^5 = 32.
#17
Level 2
What is the value of 2^2 x 3^1?
Explanation: 2^2 = 4 and 3^1 = 3, so 4 x 3 = 12.
#18
Level 2
Calculate (3^2 + 2^2) x 2.
Explanation: 3^2 = 9 and 2^2 = 4, so (9 + 4) x 2 = 26.
#19
Level 2
If 6^2 = 36, what is 6^2 ÷ 6^1?
Explanation: 6^2 ÷ 6^1 = 6^(2-1) = 6^1 = 6.
#20
Level 2
What is (5^2 - 3^2)?
Explanation: 5^2 = 25 and 3^2 = 9, so 25 - 9 = 16.
#21
Level 3
Calculate 2^3 + 2^3 x 2.
Explanation: 2^3 = 8, so 8 + 8 x 2 = 8 + 16 = 24.
#22
Level 3
What is (2^2 + 3^2) x 2?
Explanation: 2^2 = 4 and 3^2 = 9, so (4 + 9) x 2 = 26.
#23
Level 3
If 4^2 = 16, what is 4^2 - 2^3?
Explanation: 4^2 = 16 and 2^3 = 8, so 16 - 8 = 8.
#24
Level 3
Calculate 3^3 ÷ 3^1.
Explanation: 3^3 ÷ 3^1 = 3^(3-1) = 3^2 = 9.
#25
Level 3
What is the value of 2^4 - (2^2 + 2^2)?
Explanation: 2^4 = 16 and (2^2 + 2^2) = 8, so 16 - 8 = 8.
#26
Level 3
If 5^2 x 5^1 = 5^3, what is the value of 5^3?
Explanation: 5^3 = 125.
#27
Level 3
Calculate (3^2 + 3^2) ÷ 2.
Explanation: 3^2 = 9, so (9 + 9) ÷ 2 = 18 ÷ 2 = 9.
#28
Level 3
What is (2^3 + 2^2) x 2^1?
Explanation: 2^3 = 8 and 2^2 = 4, so (8 + 4) x 2 = 24.
#29
Level 3
If 4^2 + 2^3 = 24, what is 4^2?
Explanation: 4^2 = 16 and 2^3 = 8, so 16 + 8 = 24.
#30
Level 3
Calculate 10^2 - (5^2 x 2).
Explanation: 10^2 = 100 and 5^2 = 25, so 100 - (25 x 2) = 100 - 50 = 50.
#31
Level 4
What is the value of 3^3 + 2^(2 x 2)?
Explanation: 3^3 = 27 and 2^(2 x 2) = 16, so 27 + 16 = 43.
#32
Level 4
Calculate (5^2 + 5^1) x 2.
Explanation: (5^2 = 25 and 5^1 = 5), so (25 + 5) x 2 = 60.
#33
Level 4
If 2^4 = 16, what is 2^5 - 2^2?
Explanation: 2^5 = 32 and 2^2 = 4, so 32 - 4 = 28.
#34
Level 4
What is (3^2 + 3^1) x (4^2)?
Explanation: (3^2 = 9 and 3^1 = 3, so (9 + 3) x 16 = 12 x 16 = 192.
#35
Level 4
Calculate (6^2 - 5^2) ÷ 2.
Explanation: 6^2 = 36 and 5^2 = 25, so (36 - 25) ÷ 2 = 11 ÷ 2 = 5.5.
#36
Level 4
What is the value of (2^3 + 2^2 x 2^1)?
Explanation: 2^3 = 8, 2^2 = 4, and 2^1 = 2. So, 8 + 4 x 2 = 8 + 8 = 16.
#37
Level 4
If a cricket team scored 2^4 runs, how many runs did they score?
Explanation: 2^4 means 2 x 2 x 2 x 2 = 16.
#38
Level 4
Calculate 10^2 - (3^2 + 4^2).
Explanation: 10^2 = 100 and 3^2 = 9, 4^2 = 16, so 100 - (9 + 16) = 100 - 25 = 75.
#39
Level 4
What is the result of (5^2 x 4^2) ÷ 20?
Explanation: (5^2 = 25 and 4^2 = 16, so (25 x 16) ÷ 20 = 400 ÷ 20 = 20.
#40
Level 4
Calculate the value of (2^5 - 2^3) ÷ 2.
Explanation: 2^5 = 32 and 2^3 = 8, so (32 - 8) ÷ 2 = 24 ÷ 2 = 12.
{
"antigravity_content": "**Lesson Topic: Exponents**\n\n**Objective:** Understand the concept of exponents and how to work with them.\n\n---\n\n### Step 1: Check Current Understanding\n\n**Can you do this?** \nLet\u2019s start with a quick check to see what you already know. \nWhat does \\(2^3\\) mean? Can you calculate it?\n\n*(Wait for the child\u2019s response. If they struggle, provide a hint.)*\n\n---\n\n### Step 2: Introduction to Exponents\n\n**I Do:** \nAn exponent is a way to express repeated multiplication. For example, \\(2^3\\) means you multiply \\(2\\) by itself \\(3\\) times: \n\\[ \n2^3 = 2 \\times 2 \\times 2 = 8 \n\\] \nSo, the base is \\(2\\) and the exponent is \\(3\\). \n\n---\n\n### Step 3: Guided Practice\n\n**We Do:** \nLet\u2019s try another example together. \nCalculate \\(3^2\\). Remember, this means \\(3\\) multiplied by itself twice. \nWhat do we get? \n*(Guide them if they\u2019re unsure: \u201cWhat is \\(3 \\times 3\\)?\u201d)*\n\n---\n\n### Step 4: Independent Practice\n\n**You Do:** \nNow it\u2019s your turn! \nTry calculating \\(4^2\\) and \\(5^3\\) on your own. \nWrite down your answers, and remember to think about what each exponent means!\n\n*(Give them a few moments, then check their answers together.)*\n\n---\n\n### Step 5: Celebrate Effort and Strategy\n\nGreat job! Whether you got them right or not, I\u2019m really proud of how you tackled those problems. \nYou used the strategy of breaking down the multiplication, which is super helpful!\n\n---\n\n### Step 6: Additional Challenge\n\nNow, let\u0027s try something a bit harder, shall we? \nWhat is \\(2^4\\) and can you express it as repeated multiplication? \n*(This is slightly harder but still within their reach. Provide hints if they stumble.)*\n\n---\n\n### Conclusion\n\nRemember, every time we practice exponents, we\u2019re building our math skills. There\u2019s no rush; we all learn at our own pace! \nWhat was your favorite part of today\u2019s lesson? Let\u2019s keep practicing, and I\u2019m here to help whenever you need it!",
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"questions": [
{
"correct_answer": "B",
"difficulty": 1,
"explanation": "3^2 means 3 multiplied by itself, which is 3 x 3 = 9.",
"id": 1,
"options": [
"A) 3 + 3",
"B) 3 x 3",
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"question": "What does 3^2 mean?"
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"correct_answer": "B",
"difficulty": 1,
"explanation": "2^3 means 2 x 2 x 2 = 8.",
"id": 2,
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"question": "Calculate 2^3."
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"correct_answer": "A",
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"explanation": "Any number raised to the power of 1 is the number itself, so 5^1 = 5.",
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"correct_answer": "B",
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"explanation": "4^2 means 4 x 4 = 16.",
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"question": "What does 4^2 equal?"
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"question": "If a pencil costs 2^3 rupees, how much is it?"
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"correct_answer": "B",
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"explanation": "Any number raised to the power of 0 is 1, so 1^5 = 1.",
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"question": "What is 1^5?"
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"id": 7,
"options": [
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"question": "Calculate 2^0."
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{
"correct_answer": "A",
"difficulty": 1,
"explanation": "10^2 means 10 x 10 = 100.",
"id": 8,
"options": [
"A) 100",
"B) 10",
"C) 20",
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"question": "What is 10^2?"
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"correct_answer": "A",
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"explanation": "3^2 means 3 x 3 = 9.",
"id": 9,
"options": [
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"question": "If a cricket bat costs 3^2 rupees, how much is it?"
},
{
"correct_answer": "B",
"difficulty": 1,
"explanation": "Any number raised to the power of 1 is the number itself, so 6^1 = 6.",
"id": 10,
"options": [
"A) 1",
"B) 6",
"C) 0",
"D) 5"
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"question": "What does 6^1 equal?"
},
{
"correct_answer": "B",
"difficulty": 2,
"explanation": "2^2 = 4 and 3^2 = 9, so 4 + 9 = 13.",
"id": 11,
"options": [
"A) 10",
"B) 13",
"C) 12",
"D) 14"
],
"question": "Calculate 2^2 + 3^2."
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{
"correct_answer": "B",
"difficulty": 2,
"explanation": "2^3 = 8 and 2^2 = 4, so 8 + 4 = 12.",
"id": 12,
"options": [
"A) 12",
"B) 10",
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"D) 6"
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"question": "What is (2^3) + (2^2)?"
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{
"correct_answer": "A",
"difficulty": 2,
"explanation": "5^1 = 5, so 25 + 5 = 30.",
"id": 13,
"options": [
"A) 30",
"B) 29",
"C) 31",
"D) 25"
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"question": "If 5^2 = 25, what is 5^2 + 5^1?"
},
{
"correct_answer": "A",
"difficulty": 2,
"explanation": "3^2 = 9 and 2^2 = 4, so 9 - 4 = 5.",
"id": 14,
"options": [
"A) 5",
"B) 8",
"C) 7",
"D) 6"
],
"question": "Calculate 3^2 - 2^2."
},
{
"correct_answer": "D",
"difficulty": 2,
"explanation": "4^1 = 4 and 4^2 = 16, so 4 + 16 = 20.",
"id": 15,
"options": [
"A) 20",
"B) 18",
"C) 16",
"D) 17"
],
"question": "What is (4^1) + (4^2)?"
},
{
"correct_answer": "B",
"difficulty": 2,
"explanation": "2^3 * 2^2 = 2^(3+2) = 2^5 = 32.",
"id": 16,
"options": [
"A) 64",
"B) 16",
"C) 48",
"D) 32"
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"question": "If 2^3 = 8, calculate 2^3 * 2^2."
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{
"correct_answer": "A",
"difficulty": 2,
"explanation": "2^2 = 4 and 3^1 = 3, so 4 x 3 = 12.",
"id": 17,
"options": [
"A) 12",
"B) 18",
"C) 10",
"D) 8"
],
"question": "What is the value of 2^2 x 3^1?"
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"correct_answer": "C",
"difficulty": 2,
"explanation": "3^2 = 9 and 2^2 = 4, so (9 + 4) x 2 = 26.",
"id": 18,
"options": [
"A) 34",
"B) 30",
"C) 32",
"D) 28"
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"question": "Calculate (3^2 + 2^2) x 2."
},
{
"correct_answer": "A",
"difficulty": 2,
"explanation": "6^2 \u00f7 6^1 = 6^(2-1) = 6^1 = 6.",
"id": 19,
"options": [
"A) 6",
"B) 36",
"C) 30",
"D) 12"
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"question": "If 6^2 = 36, what is 6^2 \u00f7 6^1?"
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{
"correct_answer": "A",
"difficulty": 2,
"explanation": "5^2 = 25 and 3^2 = 9, so 25 - 9 = 16.",
"id": 20,
"options": [
"A) 16",
"B) 10",
"C) 20",
"D) 25"
],
"question": "What is (5^2 - 3^2)?"
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "2^3 = 8, so 8 + 8 x 2 = 8 + 16 = 24.",
"id": 21,
"options": [
"A) 24",
"B) 20",
"C) 16",
"D) 32"
],
"question": "Calculate 2^3 + 2^3 x 2."
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "2^2 = 4 and 3^2 = 9, so (4 + 9) x 2 = 26.",
"id": 22,
"options": [
"A) 26",
"B) 20",
"C) 22",
"D) 24"
],
"question": "What is (2^2 + 3^2) x 2?"
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "4^2 = 16 and 2^3 = 8, so 16 - 8 = 8.",
"id": 23,
"options": [
"A) 8",
"B) 6",
"C) 10",
"D) 12"
],
"question": "If 4^2 = 16, what is 4^2 - 2^3?"
},
{
"correct_answer": "C",
"difficulty": 3,
"explanation": "3^3 \u00f7 3^1 = 3^(3-1) = 3^2 = 9.",
"id": 24,
"options": [
"A) 8",
"B) 6",
"C) 9",
"D) 27"
],
"question": "Calculate 3^3 \u00f7 3^1."
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "2^4 = 16 and (2^2 + 2^2) = 8, so 16 - 8 = 8.",
"id": 25,
"options": [
"A) 8",
"B) 10",
"C) 6",
"D) 4"
],
"question": "What is the value of 2^4 - (2^2 + 2^2)?"
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "5^3 = 125.",
"id": 26,
"options": [
"A) 125",
"B) 150",
"C) 100",
"D) 75"
],
"question": "If 5^2 x 5^1 = 5^3, what is the value of 5^3?"
},
{
"correct_answer": "B",
"difficulty": 3,
"explanation": "3^2 = 9, so (9 + 9) \u00f7 2 = 18 \u00f7 2 = 9.",
"id": 27,
"options": [
"A) 9",
"B) 6",
"C) 12",
"D) 3"
],
"question": "Calculate (3^2 + 3^2) \u00f7 2."
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "2^3 = 8 and 2^2 = 4, so (8 + 4) x 2 = 24.",
"id": 28,
"options": [
"A) 20",
"B) 16",
"C) 18",
"D) 10"
],
"question": "What is (2^3 + 2^2) x 2^1?"
},
{
"correct_answer": "A",
"difficulty": 3,
"explanation": "4^2 = 16 and 2^3 = 8, so 16 + 8 = 24.",
"id": 29,
"options": [
"A) 16",
"B) 18",
"C) 20",
"D) 22"
],
"question": "If 4^2 + 2^3 = 24, what is 4^2?"
},
{
"correct_answer": "B",
"difficulty": 3,
"explanation": "10^2 = 100 and 5^2 = 25, so 100 - (25 x 2) = 100 - 50 = 50.",
"id": 30,
"options": [
"A) 70",
"B) 60",
"C) 80",
"D) 90"
],
"question": "Calculate 10^2 - (5^2 x 2)."
},
{
"correct_answer": "C",
"difficulty": 4,
"explanation": "3^3 = 27 and 2^(2 x 2) = 16, so 27 + 16 = 43.",
"id": 31,
"options": [
"A) 25",
"B) 30",
"C) 28",
"D) 24"
],
"question": "What is the value of 3^3 + 2^(2 x 2)?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "(5^2 = 25 and 5^1 = 5), so (25 + 5) x 2 = 60.",
"id": 32,
"options": [
"A) 50",
"B) 60",
"C) 45",
"D) 40"
],
"question": "Calculate (5^2 + 5^1) x 2."
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "2^5 = 32 and 2^2 = 4, so 32 - 4 = 28.",
"id": 33,
"options": [
"A) 12",
"B) 10",
"C) 8",
"D) 14"
],
"question": "If 2^4 = 16, what is 2^5 - 2^2?"
},
{
"correct_answer": "B",
"difficulty": 4,
"explanation": "(3^2 = 9 and 3^1 = 3, so (9 + 3) x 16 = 12 x 16 = 192.",
"id": 34,
"options": [
"A) 60",
"B) 80",
"C) 75",
"D) 70"
],
"question": "What is (3^2 + 3^1) x (4^2)?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "6^2 = 36 and 5^2 = 25, so (36 - 25) \u00f7 2 = 11 \u00f7 2 = 5.5.",
"id": 35,
"options": [
"A) 5",
"B) 6",
"C) 7",
"D) 8"
],
"question": "Calculate (6^2 - 5^2) \u00f7 2."
},
{
"correct_answer": "C",
"difficulty": 4,
"explanation": "2^3 = 8, 2^2 = 4, and 2^1 = 2. So, 8 + 4 x 2 = 8 + 8 = 16.",
"id": 36,
"options": [
"A) 16",
"B) 20",
"C) 18",
"D) 22"
],
"question": "What is the value of (2^3 + 2^2 x 2^1)?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "2^4 means 2 x 2 x 2 x 2 = 16.",
"id": 37,
"options": [
"A) 16",
"B) 18",
"C) 20",
"D) 14"
],
"question": "If a cricket team scored 2^4 runs, how many runs did they score?"
},
{
"correct_answer": "B",
"difficulty": 4,
"explanation": "10^2 = 100 and 3^2 = 9, 4^2 = 16, so 100 - (9 + 16) = 100 - 25 = 75.",
"id": 38,
"options": [
"A) 60",
"B) 62",
"C) 58",
"D) 52"
],
"question": "Calculate 10^2 - (3^2 + 4^2)."
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "(5^2 = 25 and 4^2 = 16, so (25 x 16) \u00f7 20 = 400 \u00f7 20 = 20.",
"id": 39,
"options": [
"A) 15",
"B) 20",
"C) 25",
"D) 30"
],
"question": "What is the result of (5^2 x 4^2) \u00f7 20?"
},
{
"correct_answer": "A",
"difficulty": 4,
"explanation": "2^5 = 32 and 2^3 = 8, so (32 - 8) \u00f7 2 = 24 \u00f7 2 = 12.",
"id": 40,
"options": [
"A) 10",
"B) 12",
"C) 8",
"D) 14"
],
"question": "Calculate the value of (2^5 - 2^3) \u00f7 2."
}
],
"source_ixl_skills": [
"Understanding exponents",
"Solve equations with variable exponents",
"Evaluate numerical expressions involving exponents"
],
"topic": "Exponents"
}