Simplify (3x^3y^2z^6/xy^-2z^3)^2
To simplify this expression, we need to use the rules of exponents. First, we can simplify the numerator and denominator separately by using the quotient rule:
(3x^3y^2z^6/xy^-2z^3) = 3x^(3-1)y^(2+2)z^(6-3) = 3x^2y^4z^3
Now, we can plug this simplified expression into our original expression:
(3x^3y^2z^6/xy^-2z^3)^2 = (3x^2y^4z^3)^2
To simplify this expression further, we can use the power rule:
(3x^2y^4z^3)^2 = 3^2 x^(2*2) y^(4*2) z^(3*2) = 9x^4y^8z^6
Therefore, the simplified expression is 9x^4y^8z^6.
To simplify the expression (3x^3y^2z^6/xy^-2z^3)^2, we need to apply the exponent rule for dividing powers with the same base.
First, simplify the expression inside the parentheses:
(3x^3y^2z^6/xy^-2z^3) = 3x^(3-1)y^(2-(-2))z^(6-3) = 3x^2y^4z^3.
Now, raise this simplified expression to the power of 2:
(3x^2y^4z^3)^2 = (3^2)(x^2)^2(y^4)^2(z^3)^2
= 9x^4y^8z^6.
Therefore, the simplified expression is 9x^4y^8z^6.