Question

Prove that 5^7+5^6 is divisible by 6.

Answer 1

Answer:

The Proof for $5^{7}+5^{6}\ is\ divisible\ by\ 6$ is below.

Step-by-step explanation:

To Prove:

$5^{7}+5^{6}\ is\ divisible\ by\ 6$

Proof:

We know law of indices

$a^{m}.a^{n}=a^{m+n}$

Therefore,

Step 1: Applying law of indices

$\dfrac{5^{7}+5^{6}}{6}=\dfrac{5^{6}.5^{1}+5^{6}}{6}$

Step 2: Taking common $5^{6}$ we get

$\dfrac{5^{7}+5^{6}}{6}=5^{6}\times (\dfrac{5^{1}+1}{6})$

Step 3: $5^{1} = 5$ so add 5 + 1 we get

$\dfrac{5^{7}+5^{6}}{6}=5^{6}\times \dfrac{6}{6}$

Step 4: Cancel 6 from both denominator and numerator we get

$\dfrac{5^{7}+5^{6}}{6}=5^{6}\times 1=5^{6}$ ...That is Divisible by 6 Proved