Question

How do you write $10 \times 10 \times 10 \times 10$ using exponents?

Answer 1

Hint: Here, we are required to write the given multiplication of the same number using exponents. Thus, by using the concept of exponents and by observing how many times the given number 10 is being multiplied by itself, we will be able to write this exponentially and hence, find the required answer.

Complete step by step solution:
In order to write $10 \times 10 \times 10 \times 10$ using exponents, we should know that an exponent or index or power of any number states how many times that particular number is being multiplied by itself.
As in this question, we can clearly observe that the given number 10 is being multiplied 4 times or in other words, we have to find the product of four tens being multiplied together.
Thus, instead of writing the multiplication of the same number, we can use exponents.
Since 10 is being multiplied 4 times.
Thus, we can write this as 10 to the fourth power or ${10^4}$

Therefore, using exponents, we can write $10,000 = 10 \times 10 \times 10 \times 10 = {10^4}$.

Note:
An expression that represents the repeated multiplication of the same number is known as power; whereas, when a number is written with power then the power becomes the exponent of that particular number. It shows that the number of times that particular number will be multiplied by itself. Hence, whenever we are given the multiplication of the same numbers then, we can express that number with an exponent. Also, as a fun fact, the powers of 10 are very useful to write large numbers and avoid writing lots of zeroes.