Power Numbers Quiz
Pre-Algebra
Power Numbers Quiz
• Checkpoint Assessment
Score ____ / 50
Name:
Date:
Period:
Directions: Read each problem carefully. You must show all work and calculation steps to receive full credit. Points are weighted by required work. No calculators permitted.
Part 1
Exponents, Negative Exponents & Order of Ops
8 Points (4 pts each)
1. Evaluate with negative exponent: [4 pts]
\( 24 \times 2^{-3} + (3^3 - 19) - 7^0 \)
Answer:
2. Apply negative exponent laws: [4 pts]
\( \frac{2^5 \cdot 2^{-2}}{(2^3)^2} \)
Power [2 pts]: ______ Fraction [2 pts]: ______
Part 2
Square Roots & Cube Roots
9 Points Total
3. Evaluate radical expressions: [4 pts: 2 pts each]
(a) \( \sqrt{169} - \sqrt{64} \) [2 pts]
Value:
(b) \( \sqrt[3]{-125} + 2\sqrt[3]{27} \) [2 pts]
Value:
4. Estimating non-perfect roots: [5 pts]
Given the irrational number \( \sqrt{88} \):
(a) Consecutive perfect squares 88 falls between [2 pts]:
Between and
(b) Estimate \( \sqrt{88} \) to nearest tenth [3 pts]:
Estimated value:
Part 3
Signed Decimal Operations
10 Points (5 pts each)
5. Multi-step decimal arithmetic: [5 pts]
\( (-18.4 + 9.75) \times (-2.6) \)
Final Product:
6. Signed decimal long division: [5 pts]
\( -39.78 \div 3.4 \)
Quotient:
Power Numbers Quiz • Pre-Algebra Page 1 of 2 • 27 Points Total • Turn over for Questions 7–9
Power Numbers Quiz • Page 2 (23 Points)
Student Name:
Part 4
Prime Factorization, GCF & LCM
10 Points (Question 7)
7. Prime Factorization, GCF & LCM Applications: [10 pts total]
Given the two numbers \( 24 \) and \( 36 \):
(a) Construct a factor tree or ladder for each number [5 pts: 2.5 pts each]:
Prime Factorization of 24:
\( 24 = \)
Prime Factorization of 36:
\( 36 = \)
(b) Use the prime factorizations to determine the GCF and LCM [5 pts: 2.5 pts each]:
GCF(24, 36) =
LCM(24, 36) =
Part 5
Scientific Notation & Ordering Number Forms
13 Points Total
8. Convert between standard and scientific notation: [4 pts: 1 pt each]
Standard → Scientific
(a) \( 48{,}500{,}000 = \)
(b) \( 0.00062 = \)
Scientific → Standard
(c) \( 7.04 \times 10^5 = \)
(d) \( 3.1 \times 10^{-4} = \)
9. Comparing and ordering diverse number forms: [9 pts total]
Given five values: \( \sqrt{39} \), \( 6.15 \times 10^0 \), \( \sqrt[3]{216} \), \( 6.\overline{3} \), \( 6\frac{3}{8} \)
\( \sqrt{39} \)
≈ _____
\( 6.15 \times 10^0 \)
= _____
\( \sqrt[3]{216} \)
= _____
\( 6.\overline{3} \)
≈ _____
\( 6\frac{3}{8} \)
= _____
Plot and label each value on the number line below [2 pts]:
6.0 6.1 6.2 6.3 6.4 6.5
Order (Least to Greatest) [2 pts]:
< < < <
Checklist: □ Show all steps □ Plot all 5 points on number line □ Simplify answers completely
Page 2 of 2 • 23 Points Total • End of Quiz
Power Numbers Answer Key
Teacher Key
Power Numbers Answer Key
• Solutions & Scoring
Total 50 Pts (9 Qs)
TARGET GRADE Pre-Alg / 8th
TIME ESTIMATE 25–35 Mins
PAGE 1 TOTAL 27 Pts (Qs 1–6)
PAGE 2 TOTAL 23 Pts (Qs 7–9)
Part 1
Exponents, Negative Exponents & Order of Ops
8 Pts (4 pts each)
1. \( 24 \times 2^{-3} + (3^3 - 19) - 7^0 \) [4 pts]
- Negative exponent: \( 2^{-3} = \frac{1}{2^3} = \frac{1}{8} \) [1 pt]
- Multiply: \( 24 \times \frac{1}{8} = 3 \) [1 pt]
- Parentheses: \( 3^3 - 19 = 27 - 19 = 8 \) [1 pt]
- Zero exponent & add/sub: \( 3 + 8 - 1 = \mathbf{10} \) [1 pt]
Answer: 10
2. \( \frac{2^5 \cdot 2^{-2}}{(2^3)^2} \) [4 pts]
- Numerator: \( 2^{5 + (-2)} = 2^3 \)
- Denominator: \( (2^3)^2 = 2^6 \)
- Quotient rule: \( 2^{3 - 6} = 2^{-3} \)
- Fraction value: \( \frac{1}{2^3} = \mathbf{\frac{1}{8}} \)
Power [2 pts]: \( 2^{-3} \) Fraction [2 pts]: \( \frac{1}{8} \)
Part 2
Square Roots & Cube Roots
9 Pts Total
3. Radical Expressions [4 pts: 2 pts each]
(a) \( \sqrt{169} - \sqrt{64} \) [2 pts]
\( 13 - 8 = \mathbf{5} \)
(b) \( \sqrt[3]{-125} + 2\sqrt[3]{27} \) [2 pts]
\( (-5) + 2(3) = -5 + 6 = \mathbf{1} \)
4. Estimating \( \sqrt{88} \) [5 pts]
Part (a) Perfect Squares [2 pts]
Between 81 and 100
Part (b) Nearest Tenth [3 pts]
Estimated: 9.4
Testing: \( 9.4^2 = 88.36 \) (diff 0.36) vs \( 9.3^2 = 86.49 \)
Part 3
Signed Decimal Operations
10 Pts (5 pts each)
5. \( (-18.4 + 9.75) \times (-2.6) \) [5 pts]
- Parentheses: \( -18.40 + 9.75 = -8.65 \) [2 pts]
- Multiply: \( 865 \times 26 = 22490 \) [2 pts]
- Sign & decimals: \( (-) \times (-) = (+) \) → \( \mathbf{22.49} \) [1 pt]
Product: 22.49
6. \( -39.78 \div 3.4 \) [5 pts]
- Shift decimal 1 place: \( -397.8 \div 34 \) [1 pt]
- Division steps: \( 397.8 \div 34 = 11.7 \) [3 pts]
- Sign rule: \( (-) \div (+) = (-) \) → \( \mathbf{-11.7} \) [1 pt]
Quotient: -11.7
Power Numbers Answer Key • Solutions Page 1 (Questions 1–6 • 27 Pts) Turn over for Questions 7–9 (23 Pts) & Rubric
Power Numbers Answer Key • Page 2 Solutions (Questions 7–9 • 23 Points)
