Question

What is ${{10}^{-10}}$ equals to?

Answer 1

Hint: Here we will find the value of the number given whose exponent has a negative sign. Firstly we know that when we reciprocal a number the exponent value of that number changes its sign using this concept we will write the reciprocal of the number and remove its sign. Then we will get the value in fraction but as it is not stated that value has to be in fraction we can convert the value obtained in decimal and get the desired answer.

Complete step-by-step solution:
The number is given as follows:
${{10}^{-10}}$…..$\left( 1 \right)$
Now as we know that,
${{x}^{-y}}=\dfrac{1}{{{x}^{y}}}$
Using above concept in equation (1) we get,
${{10}^{-10}}=\dfrac{1}{{{10}^{10}}}$
We can also write the value in decimal form as,
${{10}^{-10}}=\dfrac{1}{10000000000}$
$\Rightarrow {{10}^{-10}}=0.0000000001$
Hence ${{10}^{-10}}$ equals $\dfrac{1}{{{10}^{10}}}$ or $0.0000000001$.

Note: Exponent refers to how many times a number is multiplied to itself. Using exponent makes it easy to write the multiplication of the same numbers many times. Positive exponent indicates the multiplication and the negative exponent indicates the division so if a number has a negative exponent that means the particular number is divided by itself that many times. Easier way to find the value of a negative exponent is to first calculate the positive exponent value and then take the reciprocal of it. Two special case of exponent is when the value is $0$ or $1$ .If the exponent value is $0$ no matter how big or small the number is it will always be equal to $1$ similarly if the exponent value is $1$ the value of that number is the number itself.