For the $a^5$ and $b^2$ parts, use $(x^m)^n = x^{mn}$. What happens to the exponents $5$ and $2$ when you multiply them by $2/3$?

Rewrite $27$ as a power of $3$. Then use $(x^m)^n = x^{mn}$ to simplify $27^{2/3}$.

Make sure the coefficient (number in front) is fully simplified and that both variable exponents reflect multiplication by $2/3$, not just by $1/3$ or by $2$.

In Desmos, type (27*a^5*b^2)^(2/3) and then assign specific positive values to $a$ and $b$, such as a=2 and b=3, to see the numeric value of the original expression.

Enter each choice using the same values of $a$ and $b$: 9*a^(5/3)*b^(4/3), 9*a^(10/3)*b^(4/3), 18*a^(10/3)*b^(4/3), and 27^(2/3)*a^(10/3)*b^(2/3). The expression that gives exactly the same numeric result as the original for those $a$ and $b$ values is the equivalent expression.

Use the rule $(xyz)^n = x^n y^n z^n$.

Start with

Apply the $2/3$ power separately to each factor:

Use $(x^m)^n = x^{mn}$ for the variable parts.

For $a$:

For $b$:

So now the expression is

Rewrite $27$ as a power of $3$ to handle the fractional exponent:

Then

Substitute the simplified coefficient back into the expression:

So the equivalent expression is $9a^{10/3}b^{4/3}$, which matches choice B.