Simplify the following:
$ 3^{4} \times 10^{4} \times 125 \times x^{10} \p 5^{7} \times 6^{4} \times\left(x^{7}\right) $

Given:

\( 3^{4} \times 10^{4} \times 125 \times x^{10} \div 5^{7} \times 6^{4} \times\left(x^{7}\right) \)

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} 3^{4} \times 10^{4} \times 125\times x^{10} \div 5^{7} \times 6^{4} \times x^{7} =\frac{3^{4} \times ( 2\times 5)^{4} \times 5^{3} \times x^{10} \times ( 2\times 3)^{4} \times x^{7}}{5^{7}}\ =\frac{3^{4} \times 2^{4} \times 5^{4} \times 5^{3} \times x^{10} \times 2^{4} \times 3^{4} \times x^{7}}{5^{7}}\ =3^{4+4} \times 2^{4+4} \times 5^{4+3-7} \times x^{10+7}\ =3^{8} \times 2^{8} \times 5^{0} \times x^{17}\ =2^{8} \times 3^{5} \times x^{17} \end{array}$

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Updated on: 10-Oct-2022

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