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Class 8 Power Play: cheat sheet
CBSE Mathematics. 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
| Same base | aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ |
| Same power | aᵐ × bᵐ = (ab)ᵐ; aᵐ ÷ bᵐ = (a/b)ᵐ |
| Zero and negative | a⁰ = 1; a⁻ⁿ = 1/aⁿ; (a/b)⁻ⁿ = (b/a)ⁿ |
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
Find the value of (−4)⁵.
Working: 5 is odd, so the answer is negative; 4⁵ = 1024
Answer: −1024
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