Which of these is correct?

Question

A. 5^8/5^6 = 25
B. 3^6/3^4 = 1/9
C. 6^7/6^-5 = 36
D. 4^0/4^3 = 0

Answer 1

To determine which of the given options is correct, we can simplify each expression using the properties of exponents.

A. $\frac{5^8}{5^6}=5^{8-6}=5^2=25$ ✔️ (This is correct)

B. $\frac{3^6}{3^4}=3^{6-4}=3^2=9$. So, $\frac{3^6}{3^4}\ne \frac{1}{9}$. ❌ (This is incorrect)

C. $\frac{6^7}{6^{-5}}=6^{7-(-5)}=6^{7+5}=6^{12}$. $6^{12}\ne 36$. ❌ (This is incorrect)

D. $\frac{4^0}{4^3}=\frac{1}{4^3}=\frac{1}{64}$. $\frac{4^0}{4^3}\ne 0$. ❌ (This is incorrect)

The only correct statement is A: $5^8/5^6=25$.