Answer

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**Hint:**To find the unit digit of the cube of the number 27 try to find the unit digit of the cube of the number 7 which is at the unit’s place of 27. Take the product of 7 with itself and check its unit’s place digit to find the unit place digit of ${{7}^{2}}$. Now, multiply the unit place digit of ${{7}^{2}}$ with 7 and check its unit’s place digit to get the answer.

**Complete step by step answer:**

Here we have been provided with the number 27 and we are asked to find the unit place digit of the cube of this number. To find the unit place digit of ${{\left( 27 \right)}^{3}}$ we need to focus on the unit place digit of 27 which is 7.

Now, the unit place digit of ${{\left( 27 \right)}^{3}}$ will be the same as the unit place digit of ${{\left( 7 \right)}^{3}}$. So, let us find the unit place digit of ${{\left( 7 \right)}^{3}}$. We know that ${{\left( 7 \right)}^{1}}$ = 7 and it has 7 as its unit’s place. Multiplying 7 with 7 we have ${{\left( 7 \right)}^{2}}$ = 49 whose unit’s place digit is 9. Therefore, the unit’s place digit of ${{\left( 7 \right)}^{3}}$ will be the unit’s place digit of the product of 9 and 7, so we get the multiple as 63 which has 3 as its unit’s place digit.

Hence, the unit’s place digit of ${{\left( 7 \right)}^{3}}$ is 3.

**Note:**Note that here the exponent of the number is small sometimes the exponent will be large. In such cases we have to form a pattern in which the unit’s place digit repeats itself after a certain exponent. For example: - The unit place digit of ${{\left( 7 \right)}^{n}}$ will repeat itself after every value of n which will be a multiple of 4. You just need to focus on the unit place digit appearing and proceed accordingly.

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