Question

How do you simplify $\dfrac{{{w^9}}}{{{w^4}}}?$

Answer 1

Hint: We know that a part of the above given number fraction is in exponential form. An exponent refers to the number of times a number is multiplied by itself. There is base and exponent or power in this type of equation. Here, in the given question $w$ is the base and the number $9$ and $4$are the exponential power. As we know that as per the property of exponent rule if there is $\dfrac{{{a^m}}}{{{a^n}}}$ then it can be written as ${a^{m - n}}$ . When we express a number in exponential form then we can say that it’s power has been raised by the exponent.

Complete step-by-step solution:
We can simplify this by using the exponent rule $\dfrac{{{a^m}}}{{{a^n}}} = {a^{m - n}}$.
To solve exponential equations with base, use the property of power of exponential functions. Here we have $a = w$ , $m = 9$ and $n = 4$.
Now by substituting the values we get $\dfrac{{{w^9}}}{{{w^4}}} = {w^{9 - 4}}$. It gives us ${w^5}$.
Hence the required answer of the exponential form is ${w^5}$.

Note: We know that exponential equations are equations in which variables occur as exponents. The formula applied before is true for all real values of $m$ and $n$ . We should solve this kind of problem by using the properties of exponents to simplify the problem. We have to keep in mind that if there is a negative value in the power or exponent then it will reverse the number .i.e. ${m^{ - x}}$ will always be equal to $\dfrac{1}{{{m^x}}}$. We should know that the most commonly used exponential function base is the transcendental number which is denoted by $e$.