Power Play

Powers of the same base multiply and divide by adding and subtracting exponents. Negative exponents mean reciprocals; standard form writes huge and tiny numbers neatly.

Key ideas

• In aⁿ, a is the base and n the exponent: a multiplied by itself n times.
• A negative base to an even power is positive, to an odd power negative: (−2)⁴ = 16, (−2)⁵ = −32.
• a⁰ = 1 for any non-zero a.
• A negative exponent means a reciprocal: 2⁻³ = 1/8.
• Standard form is k × 10ⁿ with 1 ≤ k < 10, e.g. 384000 = 3.84 × 10⁵ and 0.00052 = 5.2 × 10⁻⁴.
• Compare numbers in standard form by their powers of 10 first.

Remember

Watch out

• Multiplying the exponents when multiplying powers: 2³ × 2⁴ = 2⁷, not 2¹².
• Reading −2⁴ as (−2)⁴: −2⁴ = −16.
• Writing standard form with k of 10 or more, such as 38.4 × 10⁴.

Worked example