Answer:
We check to verify that the step [tex]\frac{x^{-3}y^{-12}}{x^{15}y^{-15}}[/tex] is included in simplifying the expression.
Thus, option D is correct.
Step-by-step explanation:
Given the expression
[tex]\left(\frac{xy^4}{x^{-5}y^5}\right)^{-3}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]
[tex]=\frac{x^{-3}y^{-12}}{x^{15}y^{-15}}[/tex] ← This is the step
Thus, the step [tex]\frac{x^{-3}y^{-12}}{x^{15}y^{-15}}[/tex] is included in simplifying the expression.
Thus, option D is correct.
BONUS!
LET US SOLVE THE REMAINING
[tex]=\frac{x^{-3}y^{-12}}{x^{15}y^{-15}}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}[/tex]
[tex]=\frac{y^{-12}}{y^{-15}x^{15-\left(-3\right)}}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]=\frac{y^{-12-\left(-15\right)}}{x^{18}}[/tex]
[tex]=\frac{y^3}{x^{18}}[/tex]
From the above calculations, we check to verify that the step [tex]\frac{x^{-3}y^{-12}}{x^{15}y^{-15}}[/tex] is included in simplifying the expression.
Thus, option D is correct.
