How to find the value of 20 to the 56th power and the number of digits [Easy]

20 to the power of 56 is 7205759403792793600000000000000000000000000000000000000000000000000000000

The formula is shown below.

$20^{56}=$
7205759403792793600000000000000000000000000000000000000000000000000000000

Also, $20^{56}$ has 73 digits.

This time, I will explain how to find the value of $20^{56}$ and how to solve for the number of digits in $20^{56}$.

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Calculating 20 to the 56th Power

20 to the 56th power is simply 20 multiplied by 56 times.

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

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, it takes effort to calculate the power, so sometimes you need to find out how many digits the value of the power is.

Next, let's find the number of digits in $20^{56}$.

Number of digits in 20 to the 56th power

Calculating $20^{56}$ gives us 73 digits.

Find the number of digits in 20 to the 56th power

Let's calculate the common logarithm of 20 to the 56th power.

\begin{eqnarray}
\log_{10}20^{56}&=&56 \log_{10}20\\
&=&56\times 1.301\cdots\\
&=&72.857
\end{eqnarray}

In other words,
We can say that $20^{56}=10^{72.857}$, so we know that $20^{56}$ has 73 digits.

How to find the number of digits

To find the number of digits in $20^{56}$, 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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