Study guides › Level 8 · Algebra 2

Negative and fraction powers

Level 8 · Algebra 2 · for questions like “2⁻³ = ? or 8^(2/3) = ?”

💡 The idea

• A negative power means “one over”: b⁻ⁿ = 1 ÷ bⁿ.
• A fraction power is a root, then a power: b^(p/q) = (q-th root of b)ᵖ.

🪜 The steps

1. Negative power: work out the positive power, then put 1 over it.
2. Fraction power: take the root shown by the bottom number first, then raise it to the top number.

✏️ Worked examples

1. 2⁻³: 2³ = 8, so the answer is 1/8.

2. 8^(2/3): the cube root of 8 is 2, and 2² = 4.

3. 25^(3/2): the square root of 25 is 5, and 5³ = 125.

⚠️ Watch out

• A negative power never makes the number negative. 2⁻³ is 1/8, not −8.
• Root first: it keeps the numbers small.

🎯 Try these

1. 5⁻²
2. 27^(2/3)
3. 16^(3/4)

Answers: 1) 1/25 2) 9 3) 8

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.