Simplify the following
$ \left(15^{4}\right) \times 9^{4} \times 80 \p\left(12^{2}\right) \times $ $ \left(27^{2}\right) $

Given:

\( \left(15^{4}\right) \times 9^{4} \times 80 \div\left(12^{2}\right) \times \) \( \left(27^{2}\right) \)

To do:

We have to find the value of $x$.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$  

Therefore,

$ \begin{array}{l}
\left( 15^{4}\right) \times 9^{4} \times 80\div \left( 12^{2}\right) \times \left( 27^{2}\right) =\frac{( 3\times 5)^{4} \times \left( 3^{2}\right)^{4} \times \left( 2^{4} \times 5\right) \times \left( 3^{3}\right)^{2}}{\left( 2^{2} \times 3\right)^{2}}\\
=\frac{3^{4} \times 5^{4} \times 3^{2\times 4} \times 2^{4} \times 5\times 3^{3\times 2}}{2^{2\times 2} \times 3^{2}}\\
=3^{4+8+6-2} \times 5^{4+1} \times 2^{4-4}\\
=3^{16} \times 5^{5} \times 2^{0}\\
=3^{16} \times 5^{5}\\
\end{array}$

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Updated on: 10-Oct-2022

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