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Exponents and Order of Operations Practice
Fifty original questions covering the complete exponents and order of operations lesson, with explanations and SAT-focused strategy.
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Question 1
Explanation
The base is the repeated factor, \(7\); the exponent \(4\) tells how many factors appear.
Question 2
Explanation
The exponent \(5\) means \(3^5=3\cdot3\cdot3\cdot3\cdot3\). It does not mean \(3\cdot5\).
Question 3
Explanation
Five factors of \(2\) give \(2^5=2\cdot2\cdot2\cdot2\cdot2=32\).
Question 4
Explanation
Parentheses make \(-3\) the base: \((-3)(-3)=9\).
Question 5
Explanation
The exponent applies to \(3\) before the leading negative: \(-3^2=-(3^2)=-9\).
Question 6
Explanation
The repeated factor is \(5\) and it appears three times, so the power is \(5^3\).
Question 7
Explanation
Division precedes subtraction: \(6\div3=2\), then \(18-2=16\).
Question 8
Explanation
Grouping comes first: \(18-6=12\), then \(12\div3=4\).
Question 9
Explanation
Evaluate the power first: \(2^3=8\), then \(4+8=12\).
Question 10
Explanation
Multiplication and division have equal priority, so work left to right: \(24\div6=4\), then \(4\times2=8\).
Question 11
Explanation
Addition and subtraction have equal priority. Left to right: \(15-8=7\), then \(7+3=10\).
Question 12
Explanation
Grouping first gives \(2+1=3\); then \(12\div3=4\); finally \(6+4=10\).
Question 13
Explanation
First \(4-1=3\), then \(2(3)=6\), then \(5-6=-1\), and \(3(-1)=-3\).
Question 14
Explanation
Substitute with grouping: \(4^2+3=16+3=19\).
Question 15
Explanation
Because \(a=-2\), \(a^3=(-2)^3=-8\); then \(-8-1=-9\).
Question 16
Explanation
Compute grouping and power: \(6-2=4\), \(2^3=8\). Then \(4(4)=16\), and \(8+16=24\).
Question 17
Explanation
Exponent first: \(3^2=9\). Then \(36\div9=4\), and \(4+1=5\).
Question 18
Explanation
A cube has exponent \(3\), and \(4^3=64\). Although \(8^2\) is also \(64\), it is a square rather than a cube.
Question 19
Explanation
Power: \(2^2=4\). Multiplication: \(3(4)=12\). Then left to right: \(5+12-4=13\).
Question 20
Explanation
Substitute: \(2(3^2)-5(3)=2(9)-15=18-15=3\).
Question 21
Explanation
Grouping gives \(5^2=25\); separately \(2^3=8\). The difference is \(25-8=17\).
Question 22
Explanation
Division and multiplication tie, so left to right gives \(20\div5=4\), then \(4\times4=16\). Combining \(5\times4\) first causes the error.
Question 23
Explanation
Subtraction and addition tie. Left to right: \(9-4=5\), then \(5+2=7\).
Question 24
Explanation
Power first inside grouping: \(4^2=16\), so \(3+16=19\). Then \(2(19)\div5=38/5\).
Question 25
Explanation
Substitute: \(-(-3)^2+2(-3)=-9-6=-15\). The leading negative is outside the square.
Question 26
Explanation
Absolute value is a grouping operation: \(|-6|=6\), and \(2^3=8\); then \(6+8=14\).
Question 27
Explanation
The bracketed divisor is \(2(4)=8\), so \(48\div8=6\).
Question 28
Explanation
Grouping \(8-3\) first gives \(5\times2=10\). Without that grouping, multiplication happens first.
Question 29
Explanation
The exponent is the grouped expression \(q+1=4\), so \(p^{q+1}=2^4=16\).
Question 30
Explanation
Inside brackets, \(3^2=9\) and \(4(2)=8\), so the bracket is \(17\). Then \(100-2(17)=100-34=66\).
Question 31
Explanation
Any positive power of \(1\) is \(1\), so \(1^{20}=1\). The others evaluate to \(0,-1,2\).
Question 32
Explanation
\((-2)^4=16\), while \(-2^4=-16\). Therefore \(16-(-16)=32\).
Question 33
Explanation
Side length is \(9+1=10\). Perimeter is \(4(10)=40\), not the square's area.
Question 34
Explanation
Four doublings multiply the initial count by four factors of \(2\): \(3(2^4)=3(16)=48\).
Question 35
Explanation
Division/multiplication left to right: \(18\div3=6\), then \(6\times2=12\). Addition/subtraction left to right gives \(7+12-5=14\).
Question 36
Explanation
Substitute: \((-1-2)^3+4(-1)=(-3)^3-4=-27-4=-31\).
Question 37
Explanation
Parentheses make \(a+b\) the base, so the entire sum is squared. Moving the exponent to only \(b\) changes the expression.
Question 38
Explanation
Inside brackets, \(8\div2+1=4+1=5\), so \(10-5=5\). Then \(3^2(5)=9(5)=45\).
Question 39
Explanation
The correct order is power, grouped subtraction, multiplication, then addition, producing \(14\).
Question 40
Explanation
\(2^4=16\), so \(16\div2=8\). Also \(3(4-6)=3(-2)=-6\). The sum is \(2\).
Question 41
Explanation
\(3x^2=3(4)=12\), while \((3x)^2=6^2=36\). The difference is \(36-12=24\).
Question 42
Explanation
Substitute \(-2\): \(2+3(-2)^2=2+3(4)=14\). Squaring removes the negative before multiplication.
Question 43
Explanation
The innermost grouping \(4-1\) must be evaluated before its exponent and the surrounding bracket.
Question 44
Explanation
Inside grouping, \(2^3=8\), so \(12-8=4\). Then \(4^2=16\), and \(16\div4=4\).
Question 45
Explanation
Substitute: \(2^3-(-3)^2+2(2)(-3)=8-9-12=-13\).
Question 46
Explanation
The stated reasoning is wrong, but the value \(22\) is coincidentally correct: left to right gives \(12\div2=6\), \(6\times3=18\), then \(4+18=22\).
Question 47
Explanation
Only \(2x^2+7\) is quadratic with leading coefficient \(2\), and it evaluates to \(25\). The extra conditions ensure a unique answer.
Question 48
Explanation
Innermost: \(2^2-3=1\). Then \(4(1)=4\), \(3+4=7\), \(2(7)=14\), and \(1+14=15\).
Question 49
Explanation
Evaluate grouped parts: exponent \(3+1=4\), so \(2^4=16\); divisor \(5-1=4\); then \(16/4=4\).
Question 50
Explanation
Substitute: \(100(1+0.1)^2=100(1.1)^2=100(1.21)=121\). Group the growth factor before applying the exponent.
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- Question 1Exponent vocabularyEasy
- Question 2Repeated multiplicationEasy
- Question 3Evaluate powersEasy
- Question 4Signed powersEasy
- Question 5Signed powersEasy
- Question 6Write powersEasy
- Question 7Order of operationsEasy
- Question 8GroupingEasy
- Question 9Order of operationsEasy
- Question 10Equal-priority operationsEasy
- Question 11Equal-priority operationsEasy
- Question 12Nested orderEasy
- Question 13Nested groupingEasy
- Question 14Substitution with exponentsEasy
- Question 15Negative substitutionEasy
- Question 16Order of operationsMedium
- Question 17Order of operationsMedium
- Question 18Power vocabularyMedium
- Question 19Mixed operationsMedium
- Question 20Polynomial evaluationMedium
- Question 21Grouping and powersMedium
- Question 22Error analysisMedium
- Question 23Error analysisMedium
- Question 24Nested orderMedium
- Question 25Signed exponent evaluationMedium
- Question 26Absolute value and orderMedium
- Question 27Grouping as divisorMedium
- Question 28Insert groupingMedium
- Question 29Variable exponentsMedium
- Question 30Complex orderMedium
- Question 31Power patternsMedium
- Question 32Signed powersMedium
- Question 33Applied evaluationMedium
- Question 34Exponential modelingMedium
- Question 35Mixed operationsMedium
- Question 36Complex substitutionMedium
- Question 37Exponent error analysisMedium
- Question 38Nested orderMedium
- Question 39Reasoning sequenceMedium
- Question 40Mixed operationsMedium
- Question 41Compare exponent placementHard
- Question 42Applied substitutionHard
- Question 43Operation-order planningHard
- Question 44Nested power evaluationHard
- Question 45Multi-variable evaluationHard
- Question 46Method evaluationHard
- Question 47Expression classificationHard
- Question 48Complex nestingHard
- Question 49Expressions in exponentsHard
- Question 50Formula substitutionHard