Question

is five^36 fifths^4 - to 5^32

Answer 1

Let's analyze the expression you've provided: \( 5^{36} \text{ fifths }^4 - 5^{32} \).

To clarify, "fifths" generally refers to the fraction \(\frac{1}{5}\). So, "fifths^4" would mean \(\left(\frac{1}{5}\right)^4\).

Therefore, we can rewrite the expression as:

\[
5^{36} \left(\frac{1}{5}\right)^4 - 5^{32}
\]

Calculating \(\left(\frac{1}{5}\right)^4\):

\[
\left(\frac{1}{5}\right)^4 = \frac{1}{5^4} = \frac{1}{625}
\]

Now, we substitute back into the expression:

\[
5^{36} \cdot \frac{1}{625} - 5^{32}
\]

We can rewrite \(625\) as \(5^4\):

\[
= \frac{5^{36}}{5^4} - 5^{32}
\]
\[
= 5^{36-4} - 5^{32}
\]
\[
= 5^{32} - 5^{32}
\]

Now, simplifying that gives:

\[
= 0
\]

So, the final answer is:

\[
5^{36} \text{ fifths }^4 - 5^{32} = 0
\]