Question

(a^m)^n * a^mn
What is equivalent to the given expression?

Answer 1

The expression given is \((a^m)^n \times a^{mn}\).

We can simplify this step-by-step:

1. **Apply the power of a power rule**: \((a^m)^n = a^{m \cdot n}\).

So, \((a^m)^n = a^{mn}\).

2. **Substituting back into the equation** gives us:
\[
a^{mn} \times a^{mn}
\]

3. **Use the property of exponents that states \(a^x \times a^y = a^{x+y}\)**:
\[
a^{mn} \times a^{mn} = a^{mn + mn} = a^{2mn}
\]

Therefore, the equivalent expression is:

\[
\boxed{a^{2mn}}
\]