147k views
2 votes
Conner and Jana are multiplying (3⁵ * 6⁸)(3⁹ * 6¹0). Is either of them correct? Explain your reasoning.

User Notorious
by
8.5k points

1 Answer

7 votes

Final answer:

Conner and Jana must add the exponents when multiplying exponentiated numbers with the same base; the correct expression should be 3¹⁴ * 6¹⁸. If they did not do this, neither of them is correct.

Step-by-step explanation:

When multiplying exponentiated numbers with the same base, you add the exponents. In the case of Conner and Jana multiplying (3⁵ * 6⁸)(3⁹ * 6¹⁰), the first step is to combine the terms with the same base. So we'll group the terms with base 3 and those with base 6.

The correct multiplication process for the base 3 terms is 3⁵ * 3⁹, which equals 3⁵⁹ (we add the exponents, so 5 + 9 = 14), resulting in 3¹⁴. For the base 6 terms, it's 6⁸ * 6¹⁰, which equals 6⁸¹⁰ (again adding the exponents, so 8 + 10 = 18), resulting in 6¹⁸. Therefore, the entire expression simplified is 3¹⁴ * 6¹⁸.

Neither Conner nor Jana is correct if they did not perform these steps or arrived at a different result because the correct method requires the addition of exponents when multiplying exponential terms with the same base.

User Dan Belden
by
8.1k points