 Hi and welcome to the session. Let us discuss the following question. Question says, find the cube root of 13824 by prime factorization method. Now first of all, let us understand that if A and B are two integers such that A cube is equal to B, then cube root of B is equal to A. Here this symbol denotes cube root. We will use this part as our key idea to solve the given question. Let us now start with the solution. Now given number is 13824. Here we have shown prime factorization of 13824. Clearly you can see multiplying two nine times and three three times we get 13824. So prime factorization of 13824 is two multiplied by two multiplied by two multiplied by two multiplied by two multiplied by two multiplied by two multiplied by two multiplied by two multiplied by three multiplied by three multiplied by three multiplied by three. Now you already know that in the prime factorization of any number if each factor appears three times then the number is a perfect cube. Now clearly you can see all the prime factors are appearing in group of three. So one three eight two four is a perfect cube. Now we will represent one three eight two four as a perfect cube. Now we can write two cube for this triplet. Similarly we will write two cube for this triplet. This multiplication sign is as it is. Again we will write this multiplication sign as it is and we will write two cube for this triplet and this multiplication sign is as it is and for this triplet we write three cube. Now we will apply this law of exponents in these two terms and in these two terms. Now consider first two terms. Note that value of a is two and value of b is again two and value of m is three. So you can write these two terms as two multiplied by two whole raised to the power three. Now write this multiplication sign as it is. Again we will apply this law in these two terms. What do you see? Value of a is two here, value of b is three and value of m is three. So you will write it as two multiplied by three whole raised to the power three. Now two multiplied by two is four. So we write four for two multiplied by two and we will write this exponent three as it is. Now write this multiplication sign as it is. Now two multiplied by three is six. So we can write six for two multiplied by three and this exponent three is as it is. Now we will apply the same law of exponents in these two terms. What do you see? Value of a is four, value of b is six and value of m is three. So we can write this product as four multiplied by six whole raised to the power three. Now four multiplied by six is 24. So we can write 24 for four multiplied by six and this exponent three is as it is. Now we get one three eight two four is equal to 24 raised to the power three. Or we can write 24 cube is equal to one three eight two four. Now using key idea we get cube root of one three eight two four is equal to 24. From key idea we know that if a cube is equal to b then cube root of b is equal to a. So this is our required answer. This completes the session. Hope you understood the solution. Take care and bye for now.