Select the equivalent expression.start fraction, y, squared, divided by, x, to the power minus 6 , x, to the power minus 1 , y, to the power 5 , end fractionx −6 x −1 y 5 y 2 ​

Sure, let's break it down step by step.

We start with the expression:

$\frac{y^2}{x^{-6} \cdot x^{-1} \cdot y^5}$

First, simplify the exponents of $x$:

$x^{-6} \cdot x^{-1} = x^{-6 + (-1)} = x^{-7}$

Now, substitute this back into the expression:

$\frac{y^2}{x^{-7} \cdot y^5}$

Next, simplify the exponents of $y$:

$\frac{y^2}{y^5} = y^{2-5} = y^{-3}$

So the expression now is:

$\frac{y^{-3}}{x^{-7}}$

Recall that $a^{-b} = \frac{1}{a^b}$, so:

$y^{-3} = \frac{1}{y^3} \quad \text{and} \quad x^{-7} = \frac{1}{x^7}$

Thus, the expression becomes:

$\frac{\frac{1}{y^3}}{\frac{1}{x^7}} = \frac{1}{y^3} \cdot x^7 = \frac{x^7}{y^3}$

Therefore, the equivalent expression is:

$\frac{x^7}{y^3}$