EXPONENT RULES CHEAT SHEET
The Ultimate Algebra 1 & 2 Survival Guide • High School Math Essentials
Rule Name Mathematical Law Step-by-Step Example
x3 • x4
= x3+4
Product Rule xa • xb = xa+b = x7
(Add exponents when multiplying same bases)
x8 / x2
= x8-2
Quotient Rule xa / xb = xa-b = x6
(Subtract bottom exponent from top)
(x3)4
= x3 • 4
Power of a Power (xa)b = xa • b = x12
(Multiply exponents when raising to a power)
(2x)3
= 23 • x3
Power of a Product (xy)a = xaya = 8x3
(Distribute the power to everything inside)
60 = 1
0 (-25x2y)0 = 1
Zero Exponent x = 1
(Any non-zero base raised to 0 is always 1)
x-3 = 1 / x3
Negative Exponent x-a = 1 / xa 4-2 = =
(Cross the line to make the exponent positive)
↑↓ COMMON PITFALLS & MISTAKES TO AVOID
The Trap: Adding bases instead of exponents. The Trap: Forgetting to power the coefficient.
Incorrect: x2 • x3 = 2x5 Incorrect: (3x)2 = 3x2 (Correct: 9x2)
The Ultimate Algebra 1 & 2 Survival Guide • High School Math Essentials
Rule Name Mathematical Law Step-by-Step Example
x3 • x4
= x3+4
Product Rule xa • xb = xa+b = x7
(Add exponents when multiplying same bases)
x8 / x2
= x8-2
Quotient Rule xa / xb = xa-b = x6
(Subtract bottom exponent from top)
(x3)4
= x3 • 4
Power of a Power (xa)b = xa • b = x12
(Multiply exponents when raising to a power)
(2x)3
= 23 • x3
Power of a Product (xy)a = xaya = 8x3
(Distribute the power to everything inside)
60 = 1
0 (-25x2y)0 = 1
Zero Exponent x = 1
(Any non-zero base raised to 0 is always 1)
x-3 = 1 / x3
Negative Exponent x-a = 1 / xa 4-2 = =
(Cross the line to make the exponent positive)
↑↓ COMMON PITFALLS & MISTAKES TO AVOID
The Trap: Adding bases instead of exponents. The Trap: Forgetting to power the coefficient.
Incorrect: x2 • x3 = 2x5 Incorrect: (3x)2 = 3x2 (Correct: 9x2)
