Simplify (3x^4)^9 / (3^5x^6)^3  using the laws of exponents, then evaluate.    Thank you!

Expert Answers

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exponents of exponents multiply, so:

`(x^4)^9=x^(36)`

`(3^5)^3=3^(15)`

`(x^6)^3=x^(18)`

So:

`((3x^4)^9)/((3^5x^6)^3) = (3^9x^(36))/(3^(15)x^(18))`

`a^b/a^c=a^(b-c)`, so:

`(3^9)/(3^(15)) = 3^(-6)` or `1/3^6`

`(x^(36))/(x^(18))=x^(18)`

Thus:

`(3^9x^(36))/(3^(15)x^(18)) = x^(18)/3^6 = x^(18)/729`


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