Question

Simplify the following expression. Assume that the variables represent positive real numbers. ((x^((1)/(3)))^(2))/((x^(2))^((8)/(3)))

Answer 1

To simplify the expression, we can apply the power of a power rule and the quotient rule for exponents.

Step-by-step explanation:

To simplify the given expression ((x^((1)/(3)))^2)/((x^2)^((8)/(3))), we can simplify the exponents and apply the power of a power rule. First, we can rewrite the expression as (x^(2/3))^2 / (x^(2*(8)/(3))). Next, we can simplify the exponents inside the parentheses: x^(2/3 * 2/1) / x^(16/3). This simplifies to x^(4/3) / x^(16/3). Finally, we can apply the quotient rule for exponents by subtracting the exponents: x^(4/3 - 16/3) = x^(-12/3) = x^(-4). Therefore, the simplified expression is x^(-4).

Learn more about simplifying expressions