1. The problem is to understand the expression $a$ to the power $b$, which is written as $a^b$. 2. The formula for exponentiation is $a^b = \underbrace{a \times a \times \cdots \times a}_{b \text{ times}}$ when $b$ is a positive integer. 3. Important rules: - If $b=0$, then $a^0=1$ for any $a \neq 0$. - If $b$ is negative, $a^b = \frac{1}{a^{-b}}$. - If $b$ is a fraction, $a^{\frac{m}{n}} = \sqrt[n]{a^m}$. 4. For example, if $a=2$ and $b=3$, then $2^3 = 2 \times 2 \times 2 = 8$. 5. This operation is used to represent repeated multiplication of the base $a$. 6. The final answer depends on the values of $a$ and $b$ but the general concept is exponentiation as repeated multiplication.