# How to find the value of 16 to the 33th power and the number of digits [understand in 1 minute]

16 to the 33th power is 5444517870735015415413993718908291383296

The calculation formula is as follows.

$16^{33}=$
5444517870735015415413993718908291383296

Also, $16^{33}$ has 40 digits.

On this page, I will introduce how to find $16^{33}$ and how to find the number of digits of $16^{33}$.

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## Calculating 16 to the 33th Power

16 to the 33th power is simply 16 multiplied by 33 times.

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

After that, a google search is convenient for finding the answer. .

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

As you can see, calculating the exponentiation requires effort, so it may be obtained as step 1.

Next, let's find the number of digits in $16^{33}$.

## Number of digits in 16 to the 33th power

Calculating $16^{33}$ gives us 40 digits. Calculating the number of digits in 16 to the 33th power

### Find the number of digits in 16 to the 33th power

Let's calculate the common logarithm of 16 to the 33th power.

\begin{eqnarray}
\log_{10}16^{33}&=&33 \log_{10}16\\
&=&33\times 1.2041\cdots\\
&=&39.735
\end{eqnarray}

In other words,
We can say that $16^{33}=10^{39.735}$, so we know that $16^{33}$ has 40 digits.

### How to find the number of digits

To find the number of digits in $16^{33}$, 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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