Question

Find the product of all the factors of $3^{16}$

• A. $3^{33}$
• B. $3^{68}$
• C. $3^{136}$
• D. $3^{128}$

Answer 1

The correct option is C $3^{136}$

There are 17 factors of $3^{16}$ that are $3^0,3^1,3^2,3^3,3^4,\cdots 3^{16}$ . Product of factors $=3^0\times 3^1\times 3^2\times 3^3\times 3^4\cdots \times \cdot \times 3^{16}=3^{(0+1+2+3+\cdots +16)}=3^{136}$