Question

Two of the problems below are correct, and four have error. Find the two correct

Answer 1

We will check all the options.

First option:

$3^5.3^2=3^{5+2}=3^7=3^{2(3.5)}=9^{3.5}\ne9^7$

Therefore, the first option is incorrect.

2nd option:

$x^3y^2x^4=x^3x^4y^2=x^{3+4}y^2=x^7y^2$

Therefore, the 2nd option is correct.

3rd Option:

$\frac{z^3}{z^3}=z^{3-3}=z^0=1\ne0$

Therefore, the 3rd option is incorrect.

4th Option:

$\frac{7^28^3}{7^38^2}=7^{2-3}\times8^{3-2}=7^{-1}\times8=\frac{1}{7}\times8=\frac{8}{7}$

Therefore, the 4th option is correct.

5th Option:

$2^32^4=2^{3+4}=2^7\ne2^{12}$

Therefore, the 5th option is incorrect.

$\frac{6^2}{6^5}=6^{2-5}=6^{-3}=\frac{1}{6^3}\ne6^3$

Therefore, the 6th option is incorrect.