Simplify this expression:
(2/3)^2 x(6xy^-1)^3
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To simplify the expression (2/3)^2 x(6xy^-1)^3, we'll simplify each term separately and then combine them.
Let's start with (2/3)^2:
To raise a fraction to a power, we raise both the numerator and the denominator to that power separately. In this case, we raise 2 to the power of 2 and 3 to the power of 2.
(2/3)^2 = (2^2)/(3^2) = 4/9
Now let's simplify (6xy^-1)^3:
To raise a term with variables to a power, we raise each variable and coefficient to that power separately. In this case, we raise 6^3, x^3, and (y^-1)^3.
6^3 = 6 x 6 x 6 = 216
x^3 = x x x = x^3
(y^-1)^3 = y^-1 x y^-1 x y^-1 = y^(-1 x 3) = y^-3 = 1/y^3
Putting it all together, the simplified expression is:
(2/3)^2 x (6xy^-1)^3 = (4/9) x (216x^3/y^3)
Next, we can multiply the fractions by multiplying the numerators together and the denominators together:
(4/9) x (216x^3/y^3) = (4 x 216 x x^3) / (9 x y^3)
Finally, we can multiply the constants, the variables with the same base (x), and the variables with the same base (y):
(4 x 216 x x^3) / (9 x y^3) = (864x^3)/(9y^3)
So the simplified expression is 864x^3/9y^3, or equivalently, 96x^3/y^3.