Question

What is the units digit of ${\left(\frac{6^6}{6^5}\right)}^6$?

• A. $6$
• B. $4$
• C. $2$
• D. $8$

Answer 1

The correct option is A $6$

First, use the rules for combining exponents to simplify the expression.

Subtract the exponents to get $\frac{6^6}{6^5}=6^1$.

Then, raise this to the sixth power: $(6^1{)}^6=6^6$.

Ignore any digits other than the units digit.

No matter how many times you multiply $6\times 6$, the result will still end in 6. The units digit is $6$.