Questions: Simplify and rewrite answer using only positive exponents. (x^(-2) y^2 z)^3 Select one: a. x^(-6)+y^6+z^3 b. x^l y^5 z^4 c. -x^6 y^6 z^3 d. (y^6 z^3)/(x^6)

Solution Steps

To simplify the given expression \(\left(x^{-2} y^{2} z\right)^{3}\) and rewrite it using only positive exponents, we need to apply the power rule \((a^m)^n = a^{m \cdot n}\) to each term inside the parentheses. Then, we will ensure all exponents are positive.

The given expression is: \[ \left(x^{-2} y^{2} z\right)^{3} \]

We need to apply the power rule \((a^m)^n = a^{mn}\) to each term inside the parentheses.

Applying the power rule to each term: \[ (x^{-2})^3 = x^{-2 \cdot 3} = x^{-6} \] \[ (y^{2})^3 = y^{2 \cdot 3} = y^{6} \] \[ (z)^3 = z^{1 \cdot 3} = z^{3} \]

Combining the simplified terms, we get: \[ x^{-6} y^{6} z^{3} \]

To rewrite the expression using only positive exponents, we move \(x^{-6}\) to the denominator: \[ \frac{y^{6} z^{3}}{x^{6}} \]

Final Answer