The image presents two mathematical formulas regarding exponents. The first one states that $a^n \times b^n = (ab)^n$. The second one states that $\frac{a^n}{b^n} = (\frac{a}{b})^n$.

1. Problem Description

The image presents two mathematical formulas regarding exponents. The first one states that $a^n \times b^n = (ab)^n$. The second one states that $\frac{a^n}{b^n} = (\frac{a}{b})^n$.

2. Solution Steps

Both equations are fundamental exponent rules.

The first equation, $a^n \times b^n = (ab)^n$, states that when multiplying two numbers raised to the same power, you can multiply the bases and then raise the result to that power.

The second equation, $\frac{a^n}{b^n} = (\frac{a}{b})^n$, states that when dividing two numbers raised to the same power, you can divide the bases and then raise the result to that power.

3. Final Answer

$a^n \times b^n = (ab)^n$

$\frac{a^n}{b^n} = (\frac{a}{b})^n$