Question

How do you simplify $ \dfrac{{{{15}^4}}}{{15}} $ and write it using only positive exponents?

Answer 1

Hint: In this question we are asked to simplify an exponential expression and write it using positive numbers only. In order to proceed with the following question we need to know about Exponents and rules associated with them. Exponent is basically the number of times a number is multiplied with itself. There are many rules related to exponents such as Product rule, Power rule, Quotient rule, Zero rule, etc. In this question we’ll use the quotient rule, which states that while dividing two bases of the same value, by keeping the base the same, we subtract the exponent values.

Complete step-by-step answer:
We are given,
 $ \dfrac{{{{15}^4}}}{{15}} $
We’ll apply quotient rules, keeping the base same, we’ll subtract the powers.
 $ \Rightarrow \dfrac{{{a^n}}}{{{a^m}}} = {a^{n - m}} $
 $ \Rightarrow {15^{4 - 1}} = {15^3} $
 $ \Rightarrow {15^3} $
This is the required answer.
So, the correct answer is “ $ \Rightarrow {15^3} $ ”.

Note: When there is no power, power is considered to be one.
There are some special cases in exponents such as
When the exponent is $ 0 $ , the expression is always equal to $ 1 $
When the exponent is $ 1 $ , the expression is equal to the base itself, since a number multiplied by itself once is equal to the number itself.
When the exponent is negative, the result turns into a fraction.
You can have a variable as base and a number as power such as $ {a^3} $ , which basically represents $ a \times a \times a $
You can have a number as base and variable as power such as, $ {2^n} $ which basically represents that 2 has to be multiplied by itself $ n $ times.