Express the following in power notation and exponential form :
$\frac{- 729}{64}$ .

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Solution

Given number: $\frac{- 729}{64}$
Factor of $\frac{729}{64} = \frac{3 \times 3 \times 3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 2 \times 2 \times 2}$
$\Rightarrow \frac{729}{64} = \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2}$
$\Rightarrow \frac{- 729}{64} = (\frac{- 3}{2}) \times (\frac{- 3}{2}) \times (\frac{- 3}{2}) \times (\frac{- 3}{2}) \times (\frac{- 3}{2}) \times (\frac{- 3}{2})$
$\Rightarrow \frac{- 729}{64} = {(\frac{- 3}{2})}^{6}$
Hence, the exponential form of $\frac{- 729}{64}$ is ${(\frac{- 3}{2})}^{6}$ where, base is $\frac{- 3}{2}$ and power is $6$ .

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