# Calculation method of 8 to the 42th power and the number of digits [Understand in 1 minute]

Converting 8 to the 42th power to a value yields 85070591730234615865843651857942052864.

The formula is as follows.

$8^{42}=$
85070591730234615865843651857942052864

Also, $8^{42}$ has 38 digits.

This time, I will explain how to solve $8^{42}$ and how to find the number of digits in $8^{42}$.

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## Calculating 8 to the 42th Power

8 to the 42th power is simply 8 multiplied by 42 times.

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

Also, you can use google search.

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

As explained above, calculating the power takes time, so sometimes we only ask how many digits the calculation result will be.

Next, let's find the number of digits in $8^{42}$.

## Number of digits in 8 to the 42th power

Calculating $8^{42}$ gives us 38 digits. Calculating the number of digits in 8 to the 42th power

### Find the number of digits in 8 to the 42th power

Let's calculate the common logarithm of 8 to the 42th power.

\begin{eqnarray}
\log_{10}8^{42}&=&42 \log_{10}8\\
&=&42\times 0.903\cdots\\
&=&37.929
\end{eqnarray}

In other words,
We can say that $8^{42}=10^{37.929}$, so we know that $8^{42}$ has 38 digits.

### How to find the number of digits

To find the number of digits in $8^{42}$, 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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