Question

is elisa correct? if not, how can she correct her error? yes, elisa is correct. no, step 1 should be 3·7·15. no, step 2 should be 7·15⁶. no, step 3 should be 7³·15³. step 1 (7·15)³ = (7·15)·(7·15)·(7·15) step 2 = 7·7·7·15·15·15 step 3 = 7⁶·15⁶

Explanation:

Step1: Recall exponent rule for products

The power of a product rule states that \((ab)^n = a^n \cdot b^n\), and when expanding \((7\cdot15)^3\), we have \((7\cdot15)\cdot(7\cdot15)\cdot(7\cdot15)\), which can be rewritten as \((7\cdot7\cdot7)\cdot(15\cdot15\cdot15)\) (by associative and commutative properties of multiplication).

Step2: Count the number of 7s and 15s

In \((7\cdot7\cdot7)\), there are 3 factors of 7, so that's \(7^3\). In \((15\cdot15\cdot15)\), there are 3 factors of 15, so that's \(15^3\). So \((7\cdot15)^3 = 7^3 \cdot 15^3\), not \(7^6 \cdot 15^6\). So Step 3 has an error; it should be \(7^3 \cdot 15^3\) instead of \(7^6 \cdot 15^6\).

Answer:

D. No, Step 3 should be \(7^3 \cdot 15^3\). (Assuming the last option is labeled D as per the order: first option A, second B, third C, fourth D)