Discussion
6(a3b8)4 × 9(a2b2)14 is equal to.
Answer: A
The product is 3024 \(a^{5}b^{10}\). Read as printed, the 4 and the 14 multiply the two terms, so the coefficients are 6 x 4 for the first and 9 x 14 for the second.
\[ 6 \times 4 \times 9 \times 14 = 3024 \]
The powers of the same letter add when terms are multiplied.
\[ a^{3} \cdot a^{2} = a^{5} \]
\[ b^{8} \cdot b^{2} = b^{10} \]
The other options carry the same letters but coefficients 4524, 3126 and 5044, which no product of 6, 4, 9 and 14 gives. If the 4 and 14 were read as exponents, the answer would be a large power of a and b, not a^5 b^10, so only the multiplier reading fits every option.
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