# How to calculate the value of 5 to the 40th power and the number of digits [Easy to understand]

5 to the 40th power is 9094947017729282379150390625

Below is the formula.

$5^{40}=$
9094947017729282379150390625

Also, $5^{40}$ has 28 digits.

This time, I will explain how to find the value of $5^{40}$ and how to solve for the number of digits in $5^{40}$.

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## Calculating 5 to the 40th Power

5 to the 40th power is simply 5 multiplied by 40 times.

Basically, the only way to solve it is by multiplication.

Also, you can use google search.

For example, if you search for "14 to the 21st power" on google, a calculator will come up and tell you the answer.

As explained, the calculation of the power takes time, so it may be obtained as step 1.

Next, let's find the number of digits in $5^{40}$.

## Number of digits in 5 to the 40th power

Calculating $5^{40}$ gives us 28 digits.

### Find the number of digits in 5 to the 40th power

Let's calculate the common logarithm of 5 to the 40th power.

\begin{eqnarray}
\log_{10}5^{40}&=&40 \log_{10}5\\
&=&40\times 0.6989\cdots\\
&=&27.958
\end{eqnarray}

In other words,
We can say that $5^{40}=10^{27.958}$, so we know that $5^{40}$ has 28 digits.

### How to find the number of digits

To find the number of digits in $5^{40}$, use common logarithms.

By using the common logarithm, we can calculate the power of 10, so we know the number of digits.

For example, $10^1=10$ is 2 digits.
On the other hand, $10^2=100$, so 3 digits.

So $10^a$ has $10+1$ digits.
If $a$ is a decimal, the number of digits is the integer part plus 1.

$a=11.34$ will be 12 digits.

## power size quiz

Q1

Which one is bigger?

$12 ^ 5$

$5^{12}$

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