Question

How do you simplify ${100^{ - \dfrac{1}{2}}}$?

Answer 1

Hint:In this question we need to simplify a number which is given to us in exponential form. The number which we have to simplify is ${100^{ - \dfrac{1}{2}}}$. To solve this question we will use the law of exponents and know the square root of a number or method of finding the square root of a positive number. This is a very simple question to try once before looking at a complete solution.

Complete step by step solution:
Let us try to solve this question in which we need to simplify ${100^{ - \dfrac{1}{2}}}$. To solve this type of problem we need to have knowledge of exponents and its basic rules. Any number $c$ written in the form $c = {a^b}$ is in exponent from where $a$ is called base and $b$ is called exponent or power. Here are the rules of exponents we used to simplify ${100^{ - \dfrac{1}{2}}}$:
1) ${x^{ - a}} = \dfrac{1}{{{x^a}}}$
2) ${x^{ab}} = {({x^a})^b}$
Now, we apply above properties to simplify ${100^{ - \dfrac{1}{2}}}$. We first apply property $1$ of exponents, to get
${100^{ - \dfrac{1}{2}}} = \dfrac{1}{{{{100}^{\dfrac{1}{2}}}}}$
Now, we apply property $2$ exponents, to get
${100^{ - \dfrac{1}{2}}} = \dfrac{1}{{{{({{100}^{\dfrac{1}{2}}})}^1}}}$
As we know that square root of $100$is $ \pm 10$ and power of any number raised to $1$ is number itself, we get ${100^{ - \dfrac{1}{2}}} = \pm \dfrac{1}{{10}}$
Hence ${100^{ - \dfrac{1}{2}}}$ simplified to $ \pm 0.1$because we know$(\dfrac{1}{{10}} = 0.1)$.

Note: To solve this type of question we need to know the definition of exponents and the basic properties of exponents. Also to solve you have to learn square, cube, cube root and square root of a number. Exponents are usually used to write the very big numbers and small numbers. For example: distance between the moon and the earth, size of atoms. Exponents are very useful in performing mathematical operations and handling of numbers.