Exponent Rules Task Cards
Cut Along Dashed Lines • Module 1 Task Cards Page 1 of 9
Card 01 Name:
Rule: Product of Powers
\( a^m \cdot a^n = a^{m+n} \) • Add exponents when multiplying like bases
Simplify (Positive Exponents)
\( 6^3 \cdot 6^3 \)
Show Work:
Answer:
Card 02 Name:
Rule: Product of Powers
\( a^m \cdot a^n = a^{m+n} \) • A base without an exponent has power \( 1 \) (\( 2 = 2^1 \))
Simplify (Positive Exponents)
\( 2 \cdot 2^2 \)
Show Work:
Answer:
Card 03 Name:
Rule: Product of Powers
\( a^m \cdot a^n \cdot a^p = a^{m+n+p} \) • Add all exponents across matching bases
Simplify (Positive Exponents)
\( 5 \cdot 5^2 \cdot 5^2 \)
Show Work:
Answer:
Card 04 Name:
Rule: Quotient of Powers
\( \frac{a^m}{a^n} = a^{m-n} = \frac{1}{a^{n-m}} \) • Subtract exponents when dividing like bases
Simplify (Positive Exponents)
\( \frac{m}{6m^3} \)
Show Work:
Answer:
Cut Along Dashed Lines • Module 1 Task Cards Page 2 of 9
Card 05 Name:
Rule: Quotient & Coefficients
Divide numerical coefficients: \( \frac{5}{5} = 1 \). Subtract exponents: \( x^1 / x^4 = \frac{1}{x^3} \)
Simplify (Positive Exponents)
\( \frac{5x}{5x^4} \)
Show Work:
Answer:
Card 06 Name:
Rule: Quotient & Coefficients
Keep coefficients fraction \( \frac{2}{5} \). Subtract variable exponents: \( a^{4-3} = a^1 \)
Simplify (Positive Exponents)
\( \frac{2a^4}{5a^3} \)
Show Work:
Answer:
Card 07 Name:
Rule: Quotient of Powers
\( \frac{a^m}{a^n} = a^{m-n} \) • Denominator has power \( 1 \) (\( 3 = 3^1 \)); subtract \( 2 - 1 \)
Simplify (Positive Exponents)
\( \frac{3^2}{3} \)
Show Work:
Answer:
Card 08 Name:
Rule: Quotient with Greater Denominator
\( \frac{a^m}{a^n} = \frac{1}{a^{n-m}} \) • Larger power stays on bottom: \( 4 - 2 = 2 \)
Simplify (Positive Exponents)
\( \frac{4^2}{4^4} \)
Show Work:
Answer:
Cut Along Dashed Lines • Module 1 Task Cards Page 3 of 9
Card 09 Name:
Rule: Coefficients & Product Rule
Multiply numbers: \( 6 \cdot 6 = 36 \). Add variable exponents: \( k^1 \cdot k^4 = k^{1+4} \)
Simplify (Positive Exponents)
\( 6k \cdot 6k^4 \)
Show Work:
Answer:
Card 10 Name:
Rule: Coefficients & Product Rule
Multiply numbers: \( 8 \cdot 5 = 40 \). Add variable powers: \( n^3 \cdot n^1 = n^{3+1} \)
Simplify (Positive Exponents)
\( 8n^3 \cdot 5n \)
Show Work:
Answer:
Card 11 Name:
Rule: Product with Single Coefficient
Keep coefficient \( 6 \). Combine variables using product rule: \( b^3 \cdot b^4 = b^{3+4} \)
Simplify (Positive Exponents)
\( 6b^3 \cdot b^4 \)
Show Work:
Answer:
Card 12 Name:
Rule: Coefficients & Product Rule
Multiply numbers: \( 7 \cdot 8 = 56 \). Add variable powers: \( k^2 \cdot k^3 = k^{2+3} \)
Simplify (Positive Exponents)
\( 7k^2 \cdot 8k^3 \)
Show Work:
Answer:
Cut Along Dashed Lines • Module 1 Task Cards Page 4 of 9
Card 13 Name:
Rule: Negative Exponents
\( a^{-n} = \frac{1}{a^n} \) • Move only the factor with the negative power to the bottom!
Simplify (Positive Exponents)
\( 3x^3 y^{-2} \)
Show Work:
Answer:
Card 14 Name:
Rule: Negative Exponents
\( a^{-n} = \frac{1}{a^n} \) • \( 3 \) and \( x^3 \) stay in numerator; move \( y^{-4} \) down
Simplify (Positive Exponents)
\( 3x^3 y^{-4} \)
Show Work:
Answer:
Card 15 Name:
Rule: Negative Exponents
\( a^{-1} = \frac{1}{a^1} = \frac{1}{a} \) • Move \( y^{-1} \) to denominator as \( y \)
Simplify (Positive Exponents)
\( 3x^2 y^{-1} \)
Show Work:
Answer:
Card 16 Name:
Rule: Coefficient vs. Exponent
The power \( -1 \) only applies to \( m \), not \( 6 \)! So \( 6m^{-1} = \frac{6}{m} \)
Simplify (Positive Exponents)
\( 6m^{-1} \)
Show Work:
Answer:
Cut Along Dashed Lines • Module 1 Task Cards Page 5 of 9
Card 17 Name:
Rule: Power of a Product
\( (ab)^n = a^n b^n \) & \( (a^m)^n = a^{m \cdot n} \) • Apply power to \( 6 \) and multiply exponents!
Simplify (Positive Exponents)
\( (6r^3)^2 \)
Show Work:
Answer:
Card 18 Name:
Rule: Power of a Product
\( (4n^2)^3 = 4^3 \cdot n^{2 \cdot 3} \) • Calculate \( 4^3 = 64 \), then multiply power \( 2 \cdot 3 \)
Simplify (Positive Exponents)
\( (4n^2)^3 \)
Show Work:
Answer:
Card 19 Name:
Rule: Power of a Product
\( (4k^3)^3 = 4^3 \cdot k^{3 \cdot 3} \) • Power applies to both the 4 and the \( k^3 \)
Simplify (Positive Exponents)
\( (4k^3)^3 \)
Show Work:
Answer:
Card 20 Name:
Rule: Scientific Notation
\( a \times 10^n \) where \( 1 \le a < 10 \). Moving decimal right gives negative power.
Write in Scientific Notation
\( 0.331 \)
Show Work:
Answer:
Cut Along Dashed Lines • Module 1 Task Cards Page 6 of 9
Card 21 Name:
Rule: Scientific Notation (Decimals < 1)
Move decimal right until 1 non-zero digit is left of the point. Count spaces for \( -n \).
Write in Scientific Notation
\( 0.000395 \)
Show Work:
Answer:
Card 22 Name:
Rule: Scientific Notation (Numbers ≥ 10)
Move decimal point left from the end. Left movement = positive exponent (\( +n \)).
Write in Scientific Notation
\( 9400 \)
Show Work:
Answer:
Card 23 Name:
Rule: Scientific Notation (Decimals < 1)
Move decimal right until behind the digit 8. Number of moves is the negative exponent.
Write in Scientific Notation
\( 0.00008 \)
Show Work:
Answer:
Card 24 Name:
Rule: Scientific Notation (Large Numbers)
Move decimal point left until between 4 and 0: \( 4.05 \times 10^n \).
Write in Scientific Notation
\( 405000 \)
Show Work:
Answer:
Cut Along Dashed Lines • Module 1 Task Cards Page 7 of 9
Card 25 Name:
Rule: Standard Form (Zero Power)
\( 10^0 = 1 \). When exponent is \( 0 \), move the decimal point \( 0 \) spaces!
Write in Standard Form
\( 6.74 \times 10^0 \)
Show Work:
Answer:
Card 26 Name:
Rule: Standard Form (Negative Power)
Negative exponent means small number: shift decimal point LEFT \( 5 \) spaces.
Write in Standard Form
\( 8 \times 10^{-5} \)
Show Work:
Answer:
Card 27 Name:
Rule: Standard Form (Positive Power)
Positive exponent of 1 means multiply by 10: shift decimal point RIGHT \( 1 \) space.
Write in Standard Form
\( 4.5 \times 10^1 \)
Show Work:
Answer:
Card 28 Name:
Rule: Standard Form (Positive Power)
Exponent is \( 4 \): move decimal point RIGHT \( 4 \) places, filling empty spots with zeros.
Write in Standard Form
\( 2.6 \times 10^4 \)
Show Work:
Answer:
Cut Along Dashed Lines • Module 1 Task Cards Page 8 of 9
Card 29 Name:
Rule: Standard Form (Negative Power)
Exponent is \( -1 \): move decimal point LEFT \( 1 \) place from behind 8 (\( 8. \rightarrow 0.8 \)).
Write in Standard Form
\( 8 \times 10^{-1} \)
Show Work:
Answer:
Card 30 Name:
Rule: Standard Form (Negative Power)
Exponent is \( -3 \): move decimal point LEFT \( 3 \) places, adding placeholder zeros.
Write in Standard Form
\( 6.7 \times 10^{-3} \)
Show Work:
Answer:
Card 31 Name:
Rule: Standard Form (Negative Power)
Exponent is \( -3 \): move decimal point LEFT \( 3 \) places from between 7 and 2.
Write in Standard Form
\( 7.2 \times 10^{-3} \)
Show Work:
Answer:
Card 32 Name:
Rule: Standard Form (Positive Power)
Exponent is \( 3 \): move decimal point RIGHT \( 3 \) places (\( 5.3 \times 1000 \)).
Write in Standard Form
\( 5.3 \times 10^3 \)
Show Work:
Answer:
Cut Along Dashed Lines • Module 1 Task Cards Page 9 of 9
Card 33 Name:
Rule: Standard Form (Large Number)
Exponent is \( 5 \): shift decimal point RIGHT \( 5 \) places, adding 4 zeros after 3.
Write in Standard Form
\( 3.3 \times 10^5 \)
Show Work:
Answer:
Card 34 Name:
Rule: Standard Form (Zero Power)
\( 10^0 = 1 \). Multiplying by \( 10^0 \) leaves the number unchanged (\( \times 1 \)).
Write in Standard Form
\( 2.75 \times 10^0 \)
Show Work:
Answer:
Quick Guide A Exponent Laws Reference
Product Rule
\( a^m \cdot a^n = a^{m+n} \) • Add exponents
Quotient Rule
\( \frac{a^m}{a^n} = a^{m-n} \) • Subtract exponents
Negative Exponent Rule
\( a^{-n} = \frac{1}{a^n} \) • Flip position to make positive
Power of a Power Rule
\( (a^m)^n = a^{m \cdot n} \) • Multiply exponents
Student Reference Card • Keep at Desk
Quick Guide B Scientific Notation Guide
Scientific Form Structure
\( a \times 10^n \) where \( 1 \le a < 10 \)
Exactly 1 non-zero digit before decimal!
Decimal Direction Rule
Big Number (≥10):
Exponent is positive \( (+n) \)
Small Number (<1):
Exponent is negative \( (-n) \)
Zero Exponent:
\( 10^0 = 1 \) • Decimal does not move.
Student Reference Card • Keep at Desk
Exponent Rules Answer Key
Teacher Resource Module 1 Wrap-Up
Exponent Rules Answer Key
Quick-Check Solutions & Step-by-Step Guidance for Cards 01 – 19
Page 1 of 2
Product of Powers Rule \( a^m \cdot a^n = a^{m+n} \)
#01: \( 6^3 \cdot 6^3 \) \( 6^{3+3} \) \( 6^6 \)
#02: \( 2 \cdot 2^2 \) \( 2^{1+2} \) \( 2^3 \) (or 8)
#03: \( 5 \cdot 5^2 \cdot 5^2 \) \( 5^{1+2+2} \) \( 5^5 \)
#09: \( 6k \cdot 6k^4 \) \( (6 \cdot 6)(k^{1+4}) \) \( 36k^5 \)
#10: \( 8n^3 \cdot 5n \) \( (8 \cdot 5)(n^{3+1}) \) \( 40n^4 \)
#11: \( 6b^3 \cdot b^4 \) \( 6 \cdot b^{3+4} \) \( 6b^7 \)
#12: \( 7k^2 \cdot 8k^3 \) \( (7 \cdot 8)(k^{2+3}) \) \( 56k^5 \)
Power of a Product Rule \( (ab)^n = a^n b^n \)
#17: \( (6r^3)^2 \) \( 6^2 \cdot r^{3 \cdot 2} \) \( 36r^6 \)
#18: \( (4n^2)^3 \) \( 4^3 \cdot n^{2 \cdot 3} \) \( 64n^6 \)
#19: \( (4k^3)^3 \) \( 4^3 \cdot k^{3 \cdot 3} \) \( 64k^9 \)
Quotient of Powers Rule \( a^m / a^n = a^{m-n} \)
#04: \( \frac{m}{6m^3} \) \( \frac{1}{6} \cdot m^{1-3} \) \( \frac{1}{6m^2} \)
#05: \( \frac{5x}{5x^4} \) \( \frac{5}{5} \cdot x^{1-4} \) \( \frac{1}{x^3} \)
#06: \( \frac{2a^4}{5a^3} \) \( \frac{2}{5} \cdot a^{4-3} \) \( \frac{2a}{5} \)
#07: \( \frac{3^2}{3} \) \( 3^{2-1} \) \( 3 \)
#08: \( \frac{4^2}{4^4} \) \( 4^{2-4} = 4^{-2} \) \( \frac{1}{4^2} \) (\( \frac{1}{16} \))
Negative Exponents Rule \( a^{-n} = 1/a^n \)
#13: \( 3x^3 y^{-2} \) Move \( y^{-2} \) down \( \frac{3x^3}{y^2} \)
#14: \( 3x^3 y^{-4} \) Move \( y^{-4} \) down \( \frac{3x^3}{y^4} \)
#15: \( 3x^2 y^{-1} \) Move \( y^{-1} \) down \( \frac{3x^2}{y} \)
#16: \( 6m^{-1} \) Only \( m \) moves \( \frac{6}{m} \)
Check Point: Watch for students multiplying coefficients by exponents (e.g. Card 17: making \( 6^2 = 12 \) instead of \( 36 \)).
Module 1 Wrap-Up • Exponent Rules Mastery Key • Page 1 of 2
Teacher Resource Module 1 Wrap-Up
Scientific Notation Answer Key
Quick-Check Solutions & Step-by-Step Guidance for Cards 20 – 34
Page 2 of 2
Cards 20–24: Scientific Notation \( a \times 10^n \)
#20: \( 0.331 \) \( 3.31 \times 10^{-1} \)
#21: \( 0.000395 \) \( 3.95 \times 10^{-4} \)
#22: \( 9400 \) \( 9.4 \times 10^3 \)
#23: \( 0.00008 \) \( 8 \times 10^{-5} \)
#24: \( 405000 \) \( 4.05 \times 10^5 \)
Rule reminder: exactly 1 non-zero digit before decimal!
Cards 25–34: Standard Form Expand Decimal
