Question

Find the unit's digit in the product 24647^117 and 45639^118​

Answer 1

Step-by-step explanation:

117×24647n

this is the answer

Answer 2

Answer:

The unit place digit in the products $24647^{117}$ and $(45639)^{118}$ are $7$ and $1$ respectively.

Step-by-step explanation:

Consider the first product as follows:

$24647^{117}$ ...... (1)

Notice that unit place digit is $7$. Then,

$7^1=7$

$7^2=49$, here unit's digit is $9$

$7^3=343$, here unit's digit is $3$

$7^4=2401$, here unit' digit is $1$

Rewrite equation (1) as follows:

⇒ $24647^{117}=((24647)^{4})^{29}\cdot24647$

The unit place digit always remain $1$ for $(24647)^4$.

This implies unit place digit for $((24647)^{4})^{29}$ is also $1$ and unit's digit of $24647$ is $7$.

So, the unit's digit for $((24647)^{4})^{29}\cdot24647$ will be $7$.

Now, consider the the second product.

$(45639)^{118}$ ...... (2)

Notice that unit place digit is $9$. Then,

$9^1=9$

$9^2=81$, here unit's digit is $1$.

Rewrite equation (2) as follows:

⇒ $45639^{118}=((45639)^{2})^{59}$

The unit place digit always remain $1$ for $(45639)^2$.

This implies unit place digit for $((45639)^{2})^{59}$ will be $1$.

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