When you multiply expressions like $x^m$ and $x^n$ with the same base $x$, think about what happens to the exponents. Do you add, subtract, multiply, or divide them?

When you add exponents that include negative numbers (like $6$ and $-2$), treat it as normal integer addition. Write out the sums for the exponents of $a$, $b$, and $c$ separately.

After you find the combined exponent for each variable, compare those exponents with the ones in each answer choice to see which matches.

In Desmos, choose nonzero values that are not $1$ or $-1$ (to avoid accidental matches). For example, type:

• a = 2
• b = 3
• c = 5

On a new line, type the original expression using these values:

(a^-2 * b^6 * c^3) * (a^5 * b^-2 * c^-1)

Note the numerical value that Desmos gives for this line.

On separate lines, enter each answer choice using the same $a$, $b$, and $c$ values, for example:

• a^-7 * b^4 * c^4
• a^3 * b^4 * c^2
• a^3 * b^8 * c^2
• a^7 * b^4 * c^4

Compare the numerical result of each with the value from the original expression. The choice whose value matches exactly is the equivalent expression.

When you multiply powers with the same base, you add the exponents:

We will use this rule separately for $a$, $b$, and $c$.

Look at the $a$ factors:

• From the first parentheses: $a^{-2}$
• From the second parentheses: $a^{5}$

Multiply them using the rule:

So the combined $a$ part is $a^{3}$.

Now look at the $b$ factors:

• From the first parentheses: $b^{6}$
• From the second parentheses: $b^{-2}$

Multiply them:

So the combined $b$ part is $b^{4}$.

Finally, look at the $c$ factors:

• From the first parentheses: $c^{3}$
• From the second parentheses: $c^{-1}$

Multiply them:

Putting all three variables together, the product is

This matches answer choice B.