Integer powers and standard form

A power counts equal factors

3⁴ = 3 × 3 × 3 × 3 = 81, not 3 × 4. Brackets decide the base: (-3)² = 9 but -3² = -(3²) = -9.

Standard form separates scale from a leading number

4 500 000 = 4.5 × 10⁶. Standard form requires 1 ≤ A < 10 in A × 10ⁿ, with integer n.

For a small positive number, 0.00072 = 7.2 × 10⁻⁴. Four place-value reductions change 7.2 into 0.00072. The negative exponent does not make the value negative.

45 × 10⁵ has the same value as 4,500,000, but its leading number is outside the standard-form interval. Convert it to 4.5 × 10⁶.

Check your understanding 1 Value and notation are different checks

Write 0.00603 in standard form. Is 60.3 × 10⁻⁴ equal to it, and is that expression in standard form?

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6.03 × 10⁻³. The expression 60.3 × 10⁻⁴ is equal in value, but its leading number is at least 10, so it is not standard form.