Question

How do you write \[10\] to the 20th power?

Answer 1

Hint: Here, in the given question, we need to write \[10\] to the 20th power. Here, the number $10$ is the base, and the number $20$ is called the power. Power can be defined as a mathematical expression that can be used to represent exactly how many times a number should be used in a multiplication process. Power in mathematics is written as ‘raising a number to the power of any other number’. Thus any number \[a\] raised to power $n$ can be expressed as: ${a^n} = \underbrace {a \times a \times a \times ...... \times a}_{{\text{n }}times}$. Here $a$ is any number and $n$ is a natural number. ${a^n}$ is also called the $nth$ power of $a$.

Complete step-by-step answer:
We have to write \[10\] to the 20th power.
The above written statement means the number $10$ is being multiplied by itself $20$ times.
So, we can write it as
\[10\] to the $20^{th}$ power = $\underbrace {10 \times 10 \times 10 \times ...... \times 10}_{20{\text{ }}times}$
Thus, we can write \[10\] to the 20th power as ${10^{20}}$.
\[10\] to the 20th power can be written as ${10^{20}}$.

Note: Remember that, \[10\] to the 20th power and \[10\] to the negative 20th power are not the same. The negative power is almost similar to the positive power of the exponent. The only change in the negative power is that the value of the expression is the reciprocal of the value obtained in the positive case. Let us consider a base number to be $a$, and the power to be $x$. The relation between the positive and the negative expression is given as: ${a^x} = \dfrac{1}{{{a^{ - x}}}}$. Remember that the value of expression when the base is $0$ is $0$ and when base is $1$ value of expression is also $1$.