GB-13-04-001 · Negative indices

Write $21^{-2}$ as an exact fraction.

Index Laws: Numerical Negative Indices Booklet p. 17

Method

1) Write base as a fraction over 1

2) Flip the fraction to make the power positive: x⁻ᵃ = (1/x)ᵃ = 1/xᵃ

Worked Example (GB-13-04-001)

Booklet p. 17:

x^{-a} = \frac{1}{x^a}

\left(\frac{21}{1}\right)^{-2} = \left(\frac{1}{21}\right)^{2} = \frac{1^{2}}{21^{2}} = \mathbf{\frac{1}{441}}

\frac{1}{441}

1. Write as fraction

2. Flip!