Algebra & Expressions
Monomials & Exponents (Power of a Power)
A monomial is a single term with a coefficient and variables raised to whole-number exponents. The Power of a Power Rule states: (xᵃ)ᵇ = xᵃˣᵇ — when raising a power to another power, multiply the exponents.
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Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Simplify (x³)⁴
Step-by-Step Solution
Power of a Power Rule: (xᵃ)ᵇ = xᵃˣᵇ
Multiply the exponents: 3 × 4 = 12
(x³)⁴ = x¹²
Answer
x¹²
Problem
Simplify (2x²)³
Step-by-Step Solution
Apply the exponent to every factor inside the parentheses
Coefficient: 2³ = 8
Variable: (x²)³ = x²ˣ³ = x⁶
(2x²)³ = 8x⁶
Answer
8x⁶
Problem
Simplify (3x⁴y²)²
Step-by-Step Solution
Apply the exponent to every factor
Coefficient: 3² = 9
x: (x⁴)² = x⁴ˣ² = x⁸
y: (y²)² = y²ˣ² = y⁴
(3x⁴y²)² = 9x⁸y⁴
Answer
9x⁸y⁴
Problem
Simplify (x⁵)⁰
Step-by-Step Solution
Any nonzero expression raised to the power of 0 equals 1
(x⁵)⁰ = x⁵ˣ⁰ = x⁰ = 1
Answer
1
Problem
Simplify (4x³y)² · x²
Step-by-Step Solution
First apply the exponent to (4x³y)²
Coefficient: 4² = 16
x: (x³)² = x⁶
y: y² = y²
So (4x³y)² = 16x⁶y²
Now multiply by x²: 16x⁶y² · x² = 16x⁶⁺²y² = 16x⁸y²
Answer
16x⁸y²
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Simplify (x²)⁵
Simplify (y³)⁴
Simplify (x⁶)²
Simplify (2x³)²
Simplify (3y²)³
Simplify (5x⁴)²
Simplify (x²y³)⁴
Simplify (2x³y²)³
Simplify (x⁴)⁰
Simplify (4x²y)² · y³
Simplify (x³)² · (x²)³
Simplify (3x²y³)² · 2x
Finished all 12? Give yourself a pat on the back — then check your work!
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