Simplify: $4 \times( \frac{2}{3})^{4} \times 9$.

Given: $4 \times( \frac{2}{3})^{4} \times 9$.

To do: To solve $4 \times( \frac{2}{3})^{4} \times 9$.

Solution:

$4 \times( \frac{2}{3})^{4} \times 9$

$=2^2\times\frac{2^4}{3^4}\times3^2$

$=2^2\times2^4\times3^{-4}\times3^2$

$=2^{2+4}\times3^{-4+2}$

$=2^6\times3^{-2}$

$=2\times2\times2\times2\times2\times2\times3^{-2}$

$=64\times3^{-2}$

$=8^2\times3^{-2}$

$=\frac{8^2}{3^2}$

$=\frac{64}{9}$

Thus, $4 \times( \frac{2}{3})^{4} \times 9=\frac{64}{9}$.

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Updated on: 10-Oct-2022

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