Grade 9 math: Exponent laws, from the basics

If your child is working on Grade 9 math, the topic "Exponent laws, from the basics" is one of the ideas where confidence is most often won or lost. Here is what it means in plain words, a worked example you can follow together, and a few simple ways to help at home.

What Grade 9 children learn

• Read a power as repeated multiplication, and use the product, quotient and power laws
• See why a zero exponent gives 1 and a negative exponent gives a reciprocal
• Simplify expressions with numbers and several variables, and write answers with positive exponents

The key ideas

• A power is repeated multiplication: 2⁴ = 2 × 2 × 2 × 2 = 16. The base is 2 and the exponent is 4.
• Same base, multiply: add the exponents. Same base, divide: subtract the exponents. Power of a power: multiply the exponents.
• An exponent outside a bracket goes to every factor inside: (2x³)² = 4x⁶.
• Zero exponent: a⁰ = 1, because a³ ÷ a³ = a⁰ and also equals 1. Negative exponent: a⁻ⁿ = 1/aⁿ. Pattern: 2³ = 8, 2² = 4, 2¹ = 2, 2⁰ = 1, 2⁻¹ = 1/2, 2⁻² = 1/4: each step down divides by 2.
• An exponent only belongs to what is right in front of it: (−5)² = 25 but −5² = −25.

Quick examples

• (2x³)⁴ ÷ (8x⁵) = 16x¹² ÷ (8x⁵) = 2x⁷
• 5⁻² = 1/25 and (3/4)⁻² = 16/9
• (a⁴b⁻²)(a⁻¹b⁵) = a³b³
• (−5)² = 25 but −5² = −25, and 9⁰ = 1

A worked example

How to help at home

• Ask your child to explain the first step of the worked example in their own words before you show them anything.
• Work through the "Try it yourself" question together, and talk about why the answer makes sense.
• Spend a few minutes a day on the free Tutorizer "Exponents" practice. Short and regular beats long and rare.
• If a step feels shaky, go back to the key ideas above and use objects, drawings or a number line.

Try it yourself

Want a challenge?

Next steps