Simplify the expression.  `(6^4/3^2)^3`

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lemjay eNotes educator| Certified Educator

`(6^4/3^2)^3`

First, simplify the expression inside the parenthesis.
To do so, express 6 as 2*3.

`= ((2*3)^4/3^2)^3`

Then, apply the rule  `(x^m*y^n)^a=x^(a*m)*y^(a*n)` .

`= ((2^4*3^4)/3^2)^3`

Then, simplify 3^4/3^2 since they have the same base. To do so,
subtract the exponents.

`= (2^4*3^(4-2))^3`

`= (2^4*3^2)^3`

Again apply the rule `(x^m*y^n)^a=x^(a*m)*y^(a*n)` .

`= 2^(4*3) * 3^(2*3)`

`= 2^12 * 3^6`

`= 2 985 984`

Hence,` (6^4/3^2)^3` `=` 2 985 984 .

pramodpandey | Student

`(6^4/3^2)^3=((6^2)^2/3^3)^3=(36^2/3^2)^3=((36/3)^2)^3`

`(12^2)^3=12^6`

 

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