Question

A^b means a raised to power b what is the remainder when 48^565 is divided by 7

Answer 1

as (ax-1)^n/a..format if n is odd thn remainder will be a-1

so (7*7-1)^565/7 will give 7-1=6 as remainder

Answer 2

Answer:

The remainder when $48^{565}$ is divided by 7 is 6.

Step-by-step explanation:

To find : $a^b$ means a raised to power b what is the remainder when $48^{565}$ is divided by 7?

Solution :

We have to find the remainder when $48^{565}$ is divided by 7.

Applying remainder theorem,

$\frac{48^{565}}{7}=\frac{(49-1)^{565}}{7}=\frac{(7\times 7-1)^{565}}{7}$

We know, 49 is completely divide by 7 and gave remainder 0.

and $\frac{(ax-1)^n}{a}$ gives remainder -1.

i.e. $\frac{(-1)^{565}}{7}\rightarrow \frac{-1}{7}$

The required remainder is 7-1=6.

Therefore, The remainder when $48^{565}$ is divided by 7 is 6.