Rational Exponents Practice

To rewrite the expression \(100^{32}\) as a product of identical factors, we can express it using rational exponents.

First, we identify that \(100\) can be expressed as \(10^2\). Thus, we have:

\[
100^{32} = (10^2)^{32}
\]

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

\[
(10^2)^{32} = 10^{2 \cdot 32} = 10^{64}
\]

Now, to express \(10^{64}\) as a product of identical factors:

\[
10^{64} = 10 \times 10 \times 10 \times \ldots \times 10
\]

There would be \(64\) factors of \(10\).

Thus, \(100^{32}\) can be expressed as:

\[
10^{64}
\]

In simplified form, the answer is:

\[
10^{64}
\]