A product with several letters calls for the product rule for exponents: add exponents only for matching bases. Multiply the number factors separately, and count a letter with no written exponent as having exponent . Desmos can check the numeric product, but counting letter factors gives the exact answer. Keep the and counts separate.
Hints
- Hint 1
The coefficient is the number in front of the letters. Multiply the three number factors in Desmos before combining the letters. What number will go in front of the simplified expression?
- Hint 2
A letter with no written exponent, such as , means . The product rule says to add exponents when multiplying the same letter. Count the factors and factors separately.
Step-by-step
Multiply the numbers and count matching letters
Step 1Find the number in front
The coefficient is the number multiplying the letters. Type in Desmos; it shows . So goes in front of the simplified product.
- Step 2
Combine the a factors
The first and last parentheses each contain an . A bare means . The product rule adds exponents when the bases match, so combine the two factors:
Add the exponents:
- Step 3
Combine the b factors
The middle parentheses contain , and the last contain one more . Use the same product rule:
Add the exponents:
- Step 4
Put the factors together
Put the coefficient and letter factors together: . For a spot check, set and in Desmos, then type the original product and . Both show . One matching value alone isn't proof; counting the factors shows they match for every and . The equivalent expression is . Choice C.