Question

simplify.
$(3y^{2}z^{-5})^{-2}$
write your answer using only positive exponents.

Explanation:

Step1: Apply power of a product rule

$(3y^2 z^{-5})^{-2} = 3^{-2} \cdot (y^2)^{-2} \cdot (z^{-5})^{-2}$

Step2: Simplify each exponent term

$3^{-2} = \frac{1}{3^2} = \frac{1}{9}$, $(y^2)^{-2} = y^{2 \times (-2)} = y^{-4}$, $(z^{-5})^{-2} = z^{(-5) \times (-2)} = z^{10}$

Step3: Convert negative exponents to positive

$y^{-4} = \frac{1}{y^4}$

Step4: Combine all terms

$\frac{1}{9} \cdot \frac{1}{y^4} \cdot z^{10} = \frac{z^{10}}{9y^4}$

Answer:

$\frac{z^{10}}{9y^4}$