Question

simplify.
$\frac{(2y^{3})^{3}}{(3y^{7})^{2}}$
write your answer using only positive exponents.

Explanation:

Step1: Expand numerator via power rule

$(2y^3)^3 = 2^3 \cdot (y^3)^3 = 8y^{9}$

Step2: Expand denominator via power rule

$(3y^7)^2 = 3^2 \cdot (y^7)^2 = 9y^{14}$

Step3: Simplify the fraction

$\frac{8y^{9}}{9y^{14}} = \frac{8}{9} \cdot y^{9-14} = \frac{8}{9}y^{-5}$

Step4: Rewrite with positive exponents

$y^{-5} = \frac{1}{y^5}$, so $\frac{8}{9} \cdot \frac{1}{y^5} = \frac{8}{9y^5}$

Answer:

$\frac{8}{9y^5}$