Question

How do you write $5\times 5\times 5$ as an exponential?

Answer 1

Hint: To write the given multiplication of three numbers in the exponential form we are going to use the property of the exponents which says that when the base is same and the same bases are in multiplication to each other then we add the power of the bases. The mathematical form of what we have just said is as follows: $a\times a={{a}^{1+1}}={{a}^{2}}$.

Complete step by step answer:
The product of the three numbers given in the above problem is as follows:
$5\times 5\times 5$
Now, we know that when the base is the same and the bases are in multiplication form then powers get added up. The mathematical form of what we have said is as follows:
$\Rightarrow a\times a={{a}^{1+1}}={{a}^{2}}$
Now, applying the above property of exponents in the first two numbers of the above product form we get,
$\Rightarrow {{5}^{2}}\times 5$
Again, we are applying the above property of the exponents we get,
$\Rightarrow {{5}^{2+1}}={{5}^{3}}$
From the above, we have converted the given product of three numbers into exponential form which is equal to ${{5}^{3}}$.

Note:
You might be thinking why we use the exponent property to convert the given product form of the three numbers. The hint lies in the term “exponential”, in this word exponent is hidden so from this, we have used the property of the exponents in finding the exponential form of the given product form.
Also, the point to be noted that whenever you haven’t given any power to the number then the power to the number is 1. Like in the above problem, there is no power specification on the number 5 but if it is not given then it is already assumed that power of that number is 1.