Question

prove that 5^7+5^6 is divisible by 6. write your answer in exponentional form.
5^7+5^6=___ * 6

Answer 1

To prove that \( 5^7 + 5^6 \) is divisible by 6, we first factor out the common term:

\[
5^7 + 5^6 = 5^6(5 + 1) = 5^6 \cdot 6
\]

Now, since \( 6 = 2 \cdot 3 \), we need to check if \( 5^6 \) is an integer, which it certainly is, and we have already factored out \( 6 \).

Thus, we can express \( 5^7 + 5^6 \) in the required form:

\[
5^7 + 5^6 = 5^6 \cdot 6
\]

In conclusion, we can write:

\[
5^7 + 5^6 = 5^6 \cdot 6
\]

Therefore, \( 5^7 + 5^6 \) is divisible by 6, and the answer is:

\[
5^6 \cdot 6
\]