First multiply the numerical coefficients $5$ and $3$. Then, separately, figure out what happens to the exponents on $m$ and on $n$.

For the $m$ terms, you have $m^2$ and $m^1$—what is $2+1$? For the $n$ terms, you have $n^1$ and $n^3$—what is $1+3$? Then attach those exponents to $m$ and $n$ with the coefficient from Hint 2.

In Desmos, enter m = 2 and on the next line n = 3 to give $m$ and $n$ concrete values.

On a new line, type (5m^2*n)*(3m*n^3) and note the numerical result Desmos shows; this is the value of the original expression for $m=2$ and $n=3$.

On separate new lines, type each option (for example, 15m^3*n^4, 15m^2*n^4, etc.). For each one, compare its value to the value from Step 2. The correct choice is the one whose value matches the original expression exactly.

Start with the product:

Group the numerical parts together and the same variables together:

Multiply the numbers $5$ and $3$:

So the coefficient of the simplified expression will be $15$.

When you multiply powers with the same base, you add the exponents: $a^x \cdot a^y = a^{x+y}$.

• For $m$: you have $m^2 \cdot m^1$, so the exponent on $m$ will be $2+1$.
• For $n$: you have $n^1 \cdot n^3$, so the exponent on $n$ will be $1+3$.

This tells you the final powers of $m$ and $n$ in the simplified expression.

Combine the coefficient from Step 2 with the exponents found in Step 3:

• Coefficient: $15$
• Power of $m$: $2+1 = 3$, so $m^3$
• Power of $n$: $1+3 = 4$, so $n^4$

The simplified expression is $15m^3 n^4$, which matches choice A.