Express each of the following exponential expressions as a rational number. ${(\frac{4}{5})}^{10} \times {[{(\frac{4}{5})}^{2}]}^{3} \div {[{(\frac{4}{5})}^{4}]}^{4}$

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Solution

${(\frac{4}{5})}^{10} \times [{(\frac{4}{5})}^{2 \times 3}] \div [{(\frac{4}{5})}^{4 \times 4}]$
$\Rightarrow {(\frac{4}{5})}^{10} \times {(\frac{4}{5})}^{6 - 16}$
$\Rightarrow {(\frac{4}{5})}^{10 - 10}$
$= {(\frac{4}{5})}^{0} = 1$ .

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