A product with the same letter in both factors calls for the product rule for exponents: add the exponents of matching bases, including negative exponents. Work with each letter separately. Desmos can check your result at chosen values, but a numerical match alone doesn't prove two expressions are equivalent for every allowed value.
Hints
- Hint 1
For a Desmos check, choose nonzero values other than for , , and . A power of is always , so using it could hide an exponent mistake.
- Hint 2
A base is the letter being raised to a power. Pair the two powers of , then the two of , then the two of . Only matching bases can be combined by adding exponents.
- Hint 3
The product rule for exponents says . Keep a negative exponent's sign when you add: for the powers, the calculation is , not .
Step-by-step
Check, then combine matching powers
Step 1Get a Desmos check value
Choose , , and for a numerical check. These values are nonzero, as required, and none is , which could hide an exponent error. Type the three assignments and the given product. Desmos prints . Keep that value to check your result; one match won't prove equivalence.
- Step 2
Combine the powers of
The base is the letter raised to a power. When multiplying powers with the same base, add their exponents. The two powers give:
The minus sign belongs to the exponent ; it doesn't make the factor negative.
- Step 3
Combine the powers of
Apply the same addition rule to the powers:
Using would treat the product like a division.
- Step 4
Combine the powers of
Add the exponents too:
The factors are multiplied, so subtracting here would give the wrong exponent.
- Step 5
Check the combined result
The three bases now give . Type that expression in Desmos; it prints , matching the original check value. The exponent rule, not that one numerical match, shows the expressions agree for every allowed nonzero , , and . So the equivalent expression is . Choice B.