When you have $(a^m)^n$, the new exponent is $mn$. Apply this idea to both $x^{2/3}$ and $y^{-1/2}$.

After you multiply the exponents, if you get a negative exponent on $y$, recall how to rewrite a negative exponent as a positive one in a fraction.

In Desmos, type the expression with specific positive values for $x$ and $y$, such as:

Note the decimal value Desmos gives for this.

On separate lines, enter each choice using the same $x$ and $y$ values, for example:

• $2^4\cdot 3^3$
• $\dfrac{2^{12}}{3^3}$
• $\dfrac{2^4}{3^3}$
• $\dfrac{2^4}{3^{12}}$

Identify which one gives exactly the same decimal value as the original expression; that choice is the equivalent expression.

Use the rule $(ab)^n = a^n b^n$.

So,

Use the rule $(a^m)^n = a^{mn}$.

Apply it to each factor:

Compute the products in the exponents:

So the expression becomes

Use the rule $a^{-k} = \frac{1}{a^k}$.

From $x^4 y^{-3}$, the factor $y^{-3}$ moves to the denominator with a positive exponent:

So the equivalent expression is $\frac{x^4}{y^3}$.