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shutvik [7]
3 years ago
12

Find the value of the following expression:

Mathematics
1 answer:
PSYCHO15rus [73]3 years ago
4 0

(2^8 *3^{-5}*6^0)^{-2} * (3^{-2}/ 2^3)^4 * 2^{28}

\mathrm{Apply\:rule}\:a^0=1,\:a\ne \:0

6^0=1

=2^{28}\left(\frac{3^{-2}}{2^3}\right)^4\left(3^{-5}\cdot \:2^8\cdot \:1\right)^{-2}

\left(2^8\cdot \:3^{-5}\cdot \:1\right)^{-2}=\left(1\cdot \frac{256}{243}\right)^{-2}=\left(\frac{243}{256}\right)^2

\left(\frac{3^{-2}}{2^3}\right)^4=\frac{1^4}{\left(2^3\cdot \:3^2\right)^4}=\frac{1^4}{3^8\cdot \:2^{12}}

2^{28}\left(\frac{3^{-2}}{2^3}\right)^4\left(3^{-5}\cdot \:2^8\cdot \:1\right)^{-2}=\frac{243^2\cdot \:1\cdot \:2^{28}}{256^2\cdot \:3^8\cdot \:2^{12}}

=\frac{2^{16}\cdot \:243^2}{3^8\cdot \:256^2}

=\frac{2^{16}\cdot \:3^{10}}{2^{16}\cdot \:3^8}

=3^2

=9

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