Question

simplified form of 81^-5/4

Answer 1

To simplify \( 81^{-5/4} \), we can start by rewriting 81 as a power of 3:

\[
81 = 3^4
\]

Now we can substitute this into the expression:

\[
81^{-5/4} = (3^4)^{-5/4}
\]

Using the property of exponents that states \( (a^m)^n = a^{m \cdot n} \), we can simplify this further:

\[
(3^4)^{-5/4} = 3^{4 \cdot (-5/4)} = 3^{-5}
\]

Now, we express \( 3^{-5} \) in a positive exponent form:

\[
3^{-5} = \frac{1}{3^5}
\]

Next, we calculate \( 3^5 \):

\[
3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
\]

Therefore, we have:

\[
\frac{1}{3^5} = \frac{1}{243}
\]

So the simplified form of \( 81^{-5/4} \) is:

\[
\boxed{\frac{1}{243}}
\]