Question

( 9³. 9 . 9⁰ ÷ 9⁴. 9¹ )-³

simplify and calculate this algebraic expression​

Answer 1

1/729

Explanation:

According to the Order of Operations, the expression will be evaluated like this.

`\left(9^3\cdot9\cdot(9^0)/(9^4)\cdot9^1\right)^(-3)\\\\=\left(729\cdot9\cdot(1)/(6561)\cdot9\right)^(-3)\\\\=\left((6561)/(6561)\cdot9\right)^(-3)=9^(-3)=\boxed{(1)/(729)}`

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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.