Rewrite with positive exponents. Assume that even roots are of nonnegative quantities and that all denominators are nonzero.
(3y(2/3))^-3
(3Y(2/3))^-3 =
(6Y/3)^-3 =
(2Y)^-3 = 2^-3Y^-3 = 1/(2^3Y^3)=1/8Y^3.
(3y 2/3)-3
rewrite with positive exponents. assume that even roots are nonzero quantities and the denominator are nonzero
To rewrite the expression with positive exponents, we need to move the base with the negative exponent to the opposite position in the fraction and change the sign of the exponent to positive. In this case, the base is 3y(2/3), and the exponent is -3.
To move the base from the denominator to the numerator, we raise the base to the positive exponent of 3 using the rule: (a/b)^n = a^n / b^n. So, we get:
(3y(2/3))^-3 = 1 / (3y(2/3))^3
Now, to simplify further, we can raise each element of the base, 3, y, and (2/3), to the power of 3:
1 / (3y(2/3))^3 = 1 / (3^3 * y^3 * (2/3)^3)
Evaluating the powers:
1 / (27 * y^3 * (8/27))
Simplifying the expression:
1 / (216/27 * y^3)
Since 216 divided by 27 is equal to 8, we get:
1 / (8 * y^3)
Thus, the expression (3y(2/3))^-3 can be rewritten with positive exponents as 1 / (8 * y^3).