The simplification form of the provided expression is 108 after applying the integer exponent properties.
In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
We have an expression:
[tex]=\left(6^{-2}\right)\left(3^{-3}\right)\left(3\:\cdot \:6\right)^4[/tex]
[tex]=\dfrac{1}{36}\cdot \dfrac{1}{27}\left(3\cdot \:6\right)^4[/tex]
[tex]=\dfrac{1}{36}\cdot \dfrac{1}{27}\cdot \:81\cdot \:1296[/tex]
[tex]=\dfrac{1}{36}\cdot \dfrac{1}{27}\cdot \dfrac{104976}{1}[/tex]
[tex]=\dfrac{104976}{972}[/tex]
= 108
Thus, the simplification form of the provided expression is 108 after applying the integer exponent properties.
Learn more about the integer exponent here:
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