Answer:
1/729
Step-by-step explanation:
According to the Order of Operations, the expression will be evaluated like this.
[tex]\left(9^3\cdot9\cdot\dfrac{9^0}{9^4}\cdot9^1\right)^{-3}\\\\=\left(729\cdot9\cdot\dfrac{1}{6561}\cdot9\right)^{-3}\\\\=\left(\dfrac{6561}{6561}\cdot9\right)^{-3}=9^{-3}=\boxed{\dfrac{1}{729}}[/tex]
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If you were to combine exponents before doing the evaluation, you would have ...
(9^3·9^1·9^0·9^-4·9^1)^-3 = 9^((3+1+0-4+1)·(-3)) = 9^-3 = 1/729
Note that the 9^1 term in the original expression is not in the denominator. The preceding division is done before the result is multiplied by 9^1, according to the order of operations.
Some authors use the ÷ symbol to mean "everything on the left divided by everything on the right". Some students fail to put needed parentheses around denominators. As a consequence we're not sure precisely what it is we're supposed to evaluate without seeing the original typeset expression.
