Question

Conner and Jana are multiplying (3⁵6⁸)(3⁹6¹⁰).

Answer 1

Conner work is correct. Jana work is wrong

Solution:

Given that,

Conner and Jana are multiplying:

$(3^56^8)(3^96^{10})$

Given Conner's work is:

$(3^56^8)(3^96^{10}) = 3^{5+9}6^{8+10} = 3^{14}6^{18}$

We have to check if this work is correct

Yes, Conner work is correct

From given,

$(3^56^8)(3^96^{10})\\\\3^5 \times 6^8 \times 3^9 \times 6^{10}$

Use the following law of exponent

$a^m \times a^n = a^{m+n}$

Therefore,

$3^5 \times 6^8 \times 3^9 \times 6^{10} = 3^5 \times 3^9 \times 6^8 \times 6^{10} = 3^{5+9} \times 6^{8+10} = 3^{14} \times 6^{18}$

Given Jana's work is:

$(3^56^8)(3^96^{10}) = 3^{5.9}6^{8.10} = 3^{45}6^{80}$

This is incorrect

The powers of same base has to be added. But here, powers are multiplied which is wrong