Question

How do you write 125 as an exponential?

Answer 1

Hint: To write the number in exponent form we will first factorize the number into prime factors. Once we have the prime factors we will check how many times a factor is multiplied to itself and replace it by exponents hence we have the given number in exponent form.

Complete step-by-step solution:
Now let us first understand the concept of exponent.
Now exponent is nothing but a number, which shows how many times a number is multiplied by itself. This is also known as indices.
Now consider the number \[{{2}^{5}}\] this is a number in the form of exponent. Now here 2 is called the base of the number and 5 is called the power of the number and the number \[{{2}^{5}}\] is nothing but 2 multiplied 5 times. Hence we have \[{{2}^{5}}\] = 2 × 2 × 2 × 2 × 2.
Now note that any number raised to 0 is 1 and any number raised to 1 is itself. For example we have ${{2}^{0}}=1$ and ${{2}^{1}}=2$ .
Hence we can write any number in the exponent form.
To write a number in exponent form we will first factorize the number in prime factors and then check which number is multiplied by itself how many times hence we can write the number easily in exponent form.
Now consider the given number 125. We know that the prime factorization of is 5 × 5 × 5.
Hence we have to multiply 5, 3 times to get 125.
Hence we can say $125={{5}^{3}}$ .
Hence we have 125 in exponent form as ${{5}^{3}}$.

Note: Now note that the power of the number can be positive, negative or zero. If the power is negative then we make it positive by taking the number in the denominator. For example ${{2}^{-3}}=\dfrac{1}{{{2}^{3}}}$.
Also we can have the power as fractions. let us say we have a number ${{2}^{\dfrac{3}{4}}}$ then it can be written as $\sqrt[4]{{{2}^{3}}}$.