Identify the base and count how many times it is multiplied by itself.

The base is 5. It is multiplied 5 times.

$$5 \times 5 \times 5 \times 5 \times 5 = 5^5$$

The exponential form is $\boxed{5^5}$.

The base is $(-4)$. It is multiplied 3 times.

$$(-4) \times (-4) \times (-4) = (-4)^3$$

The exponential form is $\boxed{(-4)^3}$.

$$8^2 \times a^2 \times b^3 \times c^3$$

The exponential form is $\boxed{8^2 a^2 b^3 c^3}$.

The base is $\frac{1}{7}$. It is multiplied 4 times.

$$\frac{1}{7} \times \frac{1}{7} \times \frac{1}{7} \times \frac{1}{7} = \left(\frac{1}{7}\right)^4$$

The exponential form is $\boxed{\left(\frac{1}{7}\right)^4}$.

$$7^3 \times (-6)^4$$

The exponential form is $\boxed{7^3 (-6)^4}$.

$$\left(\frac{1}{3}\right)^3 \times 4^3$$

The exponential form is $\boxed{\left(\frac{1}{3}\right)^3 4^3}$.