Question

Simplify. ((u^(3))/(z^(3)))((x^(2)u^(-1))/(2z^(-3)))^(3) Write your answer using only positive exp

Answer 1

To simplify the given expression, ((u^(3))/(z^(3)))((x^(2)u^(-1))/(2z^(-3)))^(3), first, multiply the fractions, then combine like terms, and finally raise the expression to the power of 3. The simplified expression is (x^6 * u^6)/(8z^18).

Step-by-step explanation:

To simplify the given expression, we need to apply the rules of exponentiation. Let's break it down step by step:

1. First, simplify the expression inside the parentheses: ((u^3)/(z^3)) * ((x^2u^(-1))/(2z^(-3)))
2. To multiply the fractions, multiply the numerators together and the denominators together: (u^3 * x^2u^(-1))/(z^3 * 2z^(-3))
3. Combine like terms in the numerator and denominator: (x^2u^2)/(2z^6)
4. Raise the entire expression to the power of 3: [(x^2u^2)/(2z^6)]^3
5. To raise a fraction to a power, raise both the numerator and denominator to that power: (x^(2*3) * u^(2*3))/(2^(3) * z^(6*3))
6. Simplify the exponents: (x^6 * u^6)/(8z^18)

Therefore, the simplified expression is (x^6 * u^6)/(8z^18).