Question

Conner and Jana are multiplying (3^5 cdot 6^8) by (3^9 cdot 6^10). Conner's Work: ( (3^5 cdot 6^8) cdot (3^9 cdot 6^{10}) = 3^{5+9} cdot 6^{8+10} ) Jana's Work: ( (3^5 cdot 6^8) cdot (3^9 cdot 6^{10}) = 3^{5cdot9} cdot 6^{8cdot10} ) Is either of them correct? Explain your reasoning.

A. (3^{14} cdot 6^{18})

B. (3^{45} cdot 6^{80})

C. (3^{56} cdot 6^{18})

D. (3^{14} cdot 6^{28})

Answer 1

Both Conner and Jana are incorrect in their work. When multiplying exponentiated quantities, you need to multiply the base values and then add the exponents.

Step-by-step explanation:

Both Conner and Jana are incorrect in their work.

Conner's work states that (3^5 × 6^8) × (3^9 × 6^10) = 3^(5+9) × 6^(8+10) which simplifies to 3^14 × 6^18. This matches option A.

Jana's work states that (3^5 × 6^8) × (3^9 × 6^10) = 3^(5×9) × 6^(8×10) which simplifies to 3^45 × 6^80. This matches option B.

However, both Conner and Jana made a mistake by not multiplying the base values together. When multiplying exponentiated quantities, you need to multiply the base values and then add the exponents. So the correct answer is (3^5 × 3^9) × (6^8 × 6^10) = 3^(5+9) × 6^(8+10) = 3^14 × 6^18, which matches option A.