Although you have used lots of parentheses, for which you are to be applauded, you might be missing the most important pair.scarne92 said:Homework Statement
Simplify the expression completely
3(y)(1/3)-3x(y)(-2/3)(2x) / [(y)(1/3)]2
It's not a good idea to convert to radicals at this point.scarne92 said:The Attempt at a Solution
My attempt is totally wrong. I can't quit figure out what to do or where to start
3(y)(1/3)-3x(y)(-2/3)(2x) / [(y)(1/3)]2
3(y)(1/3)-6x(y)(-2/3) / y(2/3)
3√[3(y)(1/3)-6x(y)(-2/3) / y(2/3)]
3√(3) y - 3√(6x) y-2 / y2
scarne92 said:3√(3) y - 3√(6x) / y4
3√3 - 3√6x / y3
(3√3 - 3√6x / y3)3
(3-6x) / y9
scarne92 said:$$ \frac{3y^{1/3} - 3xy^{-2/3}2x}{y^{2/3}}$$
yes that is the expression, I couldn't get the LaTex to work properly, but yes.
A rational exponent is an exponent that is expressed as a fraction. It indicates that a number should be raised to a certain power and then rooted by a specific denominator. For example, 2^(3/4) means taking the fourth root of 2 and then cubing the result.
To simplify expressions with rational exponents, you can use the properties of exponents. For a^(m/n), you can rewrite it as the nth root of a^m. You can also use the rule (a^m)^n = a^(m*n) to simplify further.
A negative exponent is an exponent that is less than zero. It indicates that the base number should be divided by itself raised to the absolute value of the exponent. For example, 2^(-3) is the same as 1/(2^3) = 1/8.
To simplify expressions with negative exponents, you can use the rule a^(-n) = 1/(a^n). This means that you can move a negative exponent from the numerator to the denominator or vice versa. You can also use the properties of exponents to combine terms with the same base.
Yes, it is possible to have both rational and negative exponents in the same expression. You can use the rules for simplifying rational and negative exponents together to simplify the expression. Remember to follow the order of operations and combine like terms before simplifying the powers.